Abstract
In this paper, a fourth-order finite difference scheme that preserves the dissipation of energy for solving the 2D Benjamin-Bona-Mahony-Burgers (BBMB) equation is proposed. The scheme is three-level in time and linear-implicit. The solvability, unconditional stability and convergence are rigorously proved by the discrete energy method. The rate of convergence is of O(τ2+h4). Numerical examples are given to confirm the good accuracy and the effectiveness of the present scheme for handling the 2D homogeneous and inhomogeneous BBMB equations.
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