A new finite difference scheme for the Rosenau–Burgers equation

In this paper, a linear-implicit finite difference scheme is given for the initial-boundary problem of Rosenau–Burgers equation, which is convergent and unconditionally stable. The unique solvability of numerical solutions has been shown. A priori estimate and second-order convergence of the finite difference approximate solution are discussed using energy method. Numerical results demonstrate that the scheme is efficient and accurate.