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On the convergence of a conservative numerical scheme for the usual Rosenau-RLW equation. (English) Zbl 1252.65144
Summary: We study the initial-boundary value problem of the usual Rosenau-RLW equation by finite difference method. We design a conservative numerical scheme which preserves the original conservative properties for the equation. The scheme is three-level and linear-implicit. The unique solvability of numerical solutions has been shown. Priori estimate and second order convergence of the finite difference approximate solutions are discussed by discrete energy method. Numerical results demonstrate that the scheme is efficient and accurate.

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
Full Text: DOI
[1] Zuo, Jin-Ming; Zhang, Yao-Ming; Zhang, Tian-De, A new conservative difference scheme for the general rosenau-RLW equation, Boundary value prob., 2010, 13, (2010), Article ID 516260 · Zbl 1206.65216
[2] Zhang, F.; Peréz-Ggarcı´a, V.M.; Vázquez, L., Numerical simulation of nonlinear Schrödinger system: a new conservative scheme, Appl. math. comput., 71, 165-177, (1995) · Zbl 0832.65136
[3] Zhang, F.; Vázquez, L., Two energy conserving numerical schemes for the sine-Gordon equation, Appl. math. comput., 45, 17-30, (1991) · Zbl 0732.65107
[4] Zhang, L., A finite difference scheme for the usualized regularized long-wave equation, Appl. math. comput., 168, 962-972, (2005) · Zbl 1080.65079
[5] Wong, Y.; Chang, Q.; Gong, L., An initial-boundary value problem of a nonlinear Klein-Gordon equation, Appl. math. comput., 84, 77-93, (1997) · Zbl 0884.65091
[6] Chang, Q.-S.; Jia, E.; Sun, W., Difference schemes for solving the usualized nonlinear Schrödinger equation, J. comput. phys., 148, 397-415, (1999) · Zbl 0923.65059
[7] Wang, T.-C.; Zhang, L., Analysis of some new conservative schemes for nonlinear Schrödinger equation with wave operator, Appl. math. comput., 182, 1780-1794, (2006) · Zbl 1161.65349
[8] Wang, T.-C.; Guo, B.; Zhang, L., New conservative difference schemes for a coupled nonlinear Schrödinger system, Appl. math. comput., 217, 1604-1619, (2010) · Zbl 1205.65242
[9] Chang, Q.; Guo, B.; Jiang, H., Finite difference method for usualized Zakharov equations, Math. comput., 64, 537-553, (1995) · Zbl 0827.65138
[10] Chang, Q.S.; Jiang, H., A conservative scheme for the Zakharov equations, J. comput. phys., 113, 309-319, (1994) · Zbl 0807.76050
[11] Glassey, R.T., Convergence of an energy-preserving scheme for the Zakharov equations in one space dimension, Math. comput., 58, 83-102, (1992) · Zbl 0746.65066
[12] Hu, J.S.; Zheng, K.L., Two conservative difference schemes for the generalized rosenau equation, Boundary value prob., 2010, 18, (2010), Article ID 543503 · Zbl 1187.65090
[13] Omrani, K.; Abidi, F.; Achouri, T., A new conservative finite difference scheme for the rosenau equation, 201, 35-43, (2008) · Zbl 1156.65078
[14] Zhang, L., Convergence of a conservative difference scheme for a class of klein – gordon – schrödinger equations in one space dimension, Appl. math. comput., 163, 43-355, (2005) · Zbl 1080.65084
[15] Zhou, Y., Application of discrete functional analysis to the finite difference method, (1990), International Academy Publishers Beijing
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