A Linearized Conservative Finite Difference Scheme for the Rosenau–RLW Equation

Abstract

A novel two–level linearized conservative finite difference method is proposed for solving the initial boundary value problem of the Rosenau–RLW equation. To preserve the energy conservation property, the Crank–Nicolson scheme is employed for temporal discretization, combined with an averaging treatment of the nonlinear term between the nth and $(n+1)$th time levels. For spatial discretization, a centered symmetric scheme is adopted. Meanwhile, the discrete conservation law is presented, and the existence and uniqueness of the numerical solutions are rigorously proved. Furthermore, the convergence and stability of the scheme are analyzed using the discrete energy method. Numerical experiments validate the theoretical results.