Abstract
In this article, a high-order linearized difference scheme is presented for the periodic initial value problem of the Benjamin-Bona-Mahoney-Burgers (BBMB) equation. It is proved that the proposed scheme is uniquely solvable and unconditionally convergent, with convergence order of O(h4 + k2) in the L?-norm. An application on the regularised long wave is thoroughly studied numerically. Furthermore, interaction of solitary waves with different amplitudes is shown. The three invariants of the motion are evaluated to determine the conservation properties of the system. Numerical experiments including the comparisons with other numerical methods are reported to demonstrate the accuracy and efficiency of our difference scheme and to confirm the theoretical analysis.
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