Unconditionally Stable Difference Scheme for the Numerical Solution of Nonlinear Rosenau-KdV Equation

Document Type : Original Scientific Paper


Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, I. R. Iran


In this paper we investigate a nonlinear evolution model described by the Rosenau-KdV equation. We propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of O(τ2 + h2). Furthermore we show the existence and uniqueness of numerical solutions. Comparing the numerical results with other methods in the literature show the efficiency and high accuracy of the proposed method.


Main Subjects

1. S. K. Chung, S. N. Ha, Finite element Galerkin solutions for the Rosenau equation, Appl. Anal. 54 (1994) 39-56.
2. G. Ebadi, A. Mojaver, H. Triki, A. Yildirim, A. Biswas, Topological solitons and other solutions of the Rosenau-KdV equation with power law nonlinearity, Romanian J. Phys. 58 (2013) 3-14.
3. A. Esfahani, Solitary wave solutions for generalized Rosenau-KdV equation, Commun. Theor. Phys. 55 (2011) 396-398.
4. J. Hu, Y. Xu, B. Hu, Conservative linear difference scheme for Rosenau-KdV equation, Adv. Math. Phys. 2013, Art. ID 423718, 7 pp.
5. Y. D. Kim, H. Y. Lee, The convergence of finite element Galerkin solution for the Rosenau equation, Korean J. Comput. Appl. Math. 5 (1998) 171-180.
6. P. Rosenau, A quasi-continuous description of a nonlinear transmission line, Phys. Scr. 34 (1986) 827-829.
7. P. Rosenau, Dynamics of dense discrete systems, Progr. Theoret. Phys. 79 (1988) 1028-1042.
8. Z. Z. Sun, D. D. Zhao, On the L1 convergence of a difference scheme for coupled nonlinear Schrödinger equations, Comput. Math. Appl. 59 (2010) 3286-3300.
9. J‎. ‎M‎. ‎Zuo‎, ‎Solitons and periodic solutions ‎ for the Rosenau-KdV and Rosenau-Kawahara equations‎, ‎ Appl‎. ‎Math‎. ‎Comput. 215 (2009) 835-840.