Numerical solutions of a finite difference scheme are discussed for the KdV-like Rosenau equation
with an initial condition
and boundary conditions
This equation was modelled by P. Rosenau [Dynamics of dense discrete systems, Prog. Theoretical Phys. 79, 1028-1042 (1988)] in order to describe the dynamics of dense discrete systems.
Existence and uniqueness of the solution for the scheme are shown by using the Brouwer fixed point theorem. An a priori bound and convergence of order as well as conservation of energy of the finite difference approximate solutions are discussed with numerical examples.