Crank–Nicolson finite difference scheme for the Rosenau–Burgers equation

In this paper, a Crank–Nicolson finite difference scheme for the numerical solution of the initial-boundary value problem of Rosenau–Burgers equation is proposed. Existence and uniqueness of numerical solutions are derived. It is proved that the finite difference scheme is convergent in the order of o(τ2+h2)o(τ2+h2) and stable. Numerical simulations show that the method is efficient.