An efficient tool for solving the Rosenau–Burgers equation in two dimensions

In the present work, a linearized Crank–Nicolson difference scheme for the two-dimensional Rosenau–Burgers equation is proposed. The solvability, stability and L∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{\infty }$$\end{document} convergence have been proved by the energy method. All the outcome results are reached without any restrictions on the mesh sizes. The new scheme is shown to be second-order convergent in time and space. Some numerical examples are carried out to verify our theoretical results. The numerical checks of the linearized difference scheme are compared with the exact solutions and also compared with earlier published results. It is found that the proposed method produces more accurate results than the others available in the literature.