A new implicit energy conservative difference scheme with fourth-order accuracy for the generalized Rosenau-Kawahara-RLW equation

In the present work, a new implicit fourth-order energy conservative finite difference scheme is proposed for solving the generalized Rosenau-Kawahara-RLW equation. We first design two high-order operators to approximate the third- and fifth-order derivatives in the generalized equation, respectively. Then, the generalized Rosenau-Kawahara-RLW equation is discreted by a three-level implicit finite difference technique in time, and a fourth-order accurate in space. Furthermore, we prove that the new scheme is energy conserved, unconditionally stable, and convergent with O(tau(2)+h(4)). Finally, two numerical experiments are carried out to show that the present scheme is efficient, reliable, high-order accurate, and can be used to study the solitary wave at long time.