A new high-order accurate difference scheme for the Benjamin-Bona-Mahoney-Burgers (BBMB) equation

Abstract

Inthisarticle, ahigh-orderlinearizeddifferenceschemeispresentedfortheperiodicinitialvalue
problemoftheBenjamin-Bona-Mahoney-Burgers(BBMB)equation. Itisprovedthattheproposed
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.