High-Order Non-Reflecting Boundary Conditions for Dispersive Waves

Abstract

Problems of linear time-dependent dispersive waves in an unbounded domain are con- sidered. The infinite domain is truncated via an artificial boundary B, and a high-order Non-Reflecting Boundary Condition (NRBC) is imposed on B. Then the problem is solved by a Finite Difference scheme in the finite domain bounded by 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 param- eters appearing in the NRBC is proposed. The performance of the scheme is demonstrated via numerical examples.