High-order nonreflecting boundary conditions for the dispersive shallow water equations

Time-dependent dispersive shallow water waves in an unbounded domain are considered. The infinite domain is truncated via an artificial boundary $\text{B}$, and a high-order non-reflecting boundary condition (NRBC) is imposed on $\text{B}$. Then the problem is solved by a finite difference scheme in the finite domain bounded by $\text{B}$. The sequence of NRBCs proposed by Higdon is used. However, in contrast to the original low-order implementation of the Higdon conditions, a new scheme is devised which allows the easy use of a Higdon-type NRBC of any desired order. In addition, a procedure for the automatic choice of the parameters appearing in the NRBC is proposed. The performance of the scheme is demonstrated via a numerical example.