Beschreibung:
<jats:title>Abstract</jats:title><jats:p>This paper studied a linearized conservative high‐order finite difference scheme for a model of nonlinear dispersive equation: the regularized long wave‐Korteweg de Vries (RLW‐KdV) equation. The scheme is proved to be conservative, uniquely solvable, and conditionally stable. The convergence of the difference scheme is proved by using the energy method to be of fourth‐order in space and second‐order in time in the discrete ‐norm. An application on the regularized long wave and the modified regularized long wave equations are discussed numerically in details. Furthermore, interaction of solitary waves with different amplitudes is shown. The three invariants of the motion are evaluated to determine the conservation proprieties of the system. Several numerical examples are presented in order to validate the theoretical results and compared with other existing methods. Comparison reveals that our linearized difference improves the accuracy and shortens computation time largely.</jats:p>