On the convergence of conservative difference schemes for the 2D generalized Rosenau–Korteweg de Vries equation

Two conservative finite difference schemes for the Rosenau–KdV equation (RKdV) in 2D are proposed. The first scheme is two-level and nonlinear implicit. The second scheme is three-level and linear-implicit. Existence of its difference solutions has been shown. It is proved by the discrete energy method that the two schemes are uniquely solvable, unconditionally stable, and the convergence is of second order in the uniform norm. Numerical experiments demonstrate that the schemes are accurate and efficient.