The author develops radiation boundary conditions for the numerical mo
deling of dispersive waves. During the construction of such boundary c
onditions, the goal is to simulate the outward radiation of waves near
an artificial computational boundary. The velocities of the outgoing
waves are typically involved in processes of this nature. A central pr
oblem in the dispersive case is that two different types of velocities
are present, phase velocity and group velocity, and each can vary wit
h wavenumber and frequency. With the boundary conditions developed in
this paper, the user needs to specify some parameters; in the cases th
at are emphasized here, the parameters can be interpreted in terms of
phase velocities of waves that are absorbed exactly at the computation
al boundary. The amount of reflected error is a continuous function of
the parameters, and the performance of the boundary conditions is not
sensitive to the choice of parameters. Good performance is obtained i
n numerical tests involving data that have broad bands in wavenumber s
pace. The formulas for boundary conditions are based on compositions o
f simple first-order differential operators; the same formulas can be
applied without modification to problems in both one and several dimen
sions.