The numerical solution for an homogeneous boundary conditions of generalized Rosenau - Kawahara equation is considered.A nonlinear two-level Crank-Nicolson difference scheme is designed.The difference scheme simulates the conservation properties of the problem well.The prior estimate, existence and uniqueness of the finite difference solution are also obtained. It is proved that the finite difference scheme is convergent with second-order and unconditionally stable by discrete functional analysis method.The numerical example show this scheme is feasible.
