Conservative and fourth-order compact difference schemes for the generalized Rosenau–Kawahara–RLW equation

Abstract

In this article, we present two conservative and fourth-order compact finite-difference schemes for solving the generalized Rosenau–Kawahara–RLW equation. The proposed schemes are energy-conserved, convergent, and unconditionally stable, and the numerical convergence orders in both $$l_{2}$$ -norm and $$l_{\infty }$$ -norm are of $$O(\tau ^{2}+h^{4})$$ . Numerical experiments demonstrate that the present schemes are efficient and reliable.