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 In this paper, a finite difference method for the regularized long-wave equation is considered. We propose an energy-conserved finite difference scheme. It is proved that the finite difference scheme is stable and converges in the order O(h+\tau). We also report several numerical results which show that our method is reliable.
 1 Introduction 32 Preliminaries 4 2.1 Zhang’s scheme for (5) [10] 4 2.2 Koide’s and Furihata’s schemes for (1) [5]53 Conservative schemes 84 Convergence and stability 95 Numerical simulations 126 Conclusion 12 Reference 13
 [1] T. Achouri, N. Khiari and K. Omrani, On the convergence of difference schemes for the Benjamin-Bona-Mahony (BBM) equation, Appl. Math. Comput. 182 (2006) 999–1005.[2] T.B. Benjamin, J.L. Bna and J.J. Mahony, Model equations for long waves in nonlinear dispersive systems, Philos. Trans. R. Soc. London Ser. A. 272 47–78 (1972).[3] J.C. Eilbeck and G.R. McGuire, Numerical study of the regularized long-wave equation, I: Numerical methods, J. Comput. Phys. 19 43–57 (1975).[4] J.C. Eilbeck and G.R. McGuire, Numerical study of the regularized long-wave equation, II: Numerical methods, J. Comput. Phys. 23 63–73 (1977).[5] S. Koide, D. Furihata, Nonlinear and Linear Conservative Finite Difference Schemes for Regularized Long Wave Equaion, Japan J. Indust. Appl. Math. 26 15–40 (2009).[6] K. Omrani, F. Abidi, T. Achouri, N. Khiari, A new conservative finite difference scheme for the Rosenau equation, Appl. Math. Comput. 201 35–43 (2008).[7] P.J. Olver, Euler operators and conservation laws of the BBM equation, Math. Proc. Camb. Phil. Soc. 85 143–160 (1979).[8] P. Rosenau, Dynamics of the dense discrete systems, Prog. Theor. Phys. 79 (1988) 1028–1042.[9] DU Yu, XU You-Cai, HU Bing, Three Level Finite Difference Scheme For Rosenau-Burgers Equation, Journal of Sichuan University (Natural Science Edition) 47 1–6 (2010).[10] L. Zhang, A finite difference scheme for generalized regularized long-wave equation, Appl. Math. Comput. 168 962–972 (2005).
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