Two High-Accuracy Linear Finite Difference Schemes for Rosenau–KdV–RLW Equation

Two numerical methods are investigated for the initial–boundary value problem of a nonlinear Rosenau–KdV–RLW equation with homogeneous boundary conditions. With the premise of achieving second-order theoretical accuracy in the temporal direction, two-level linearization discretization and three-level extrapolated linearization discretization are applied to nonlinear terms, respectively. To achieve a higher theoretical accuracy in the spatial direction, the Richardson extrapolation combination technique is employed; thereby, a two-level linearized difference scheme and a three-level linear difference scheme for the Rosenau–KdV–RLW equation are proposed, both with a theoretical accuracy of O(τ2+h4). The two-level difference scheme also reasonably simulates the conservation property of the problem. The convergence and stability of the two schemes are proven using mathematical induction and discrete functional analysis methods. The numerical results demonstrate the effectiveness of both schemes.