A New Nonlinear Conservative Difference Scheme for Generalized Rosenau-Kawahara Equation

Abstract

In this paper, we first propose a two-level nonlinear conservative difference scheme for solving the generalized Rosenau-Kawahara equation. The second-order convergence in $L_\infty$-norm of the scheme is proved by an induction argument and discrete energy method. And the the prior estimate in $L_\infty$-norm of the finite difference solutions is obtained. Moreover, the existence, uniqueness and stability of the numerical solution are also shown. Finally, numerical experiments indicate the new scheme is reliable and significantly reduces the CPU time.