  Hawking radiation has become experimentally testable thanks to the many
analogue systems which mimic the effects of the event horizon on wave
propagation. These systems are typically dominated by dispersion, and give rise
to a numerically soluble and stable ODE only if the rest-frame dispersion
relation $\Omega^{2}(k)$ is a polynomial of relatively low degree. Here we
present a new method for the calculation of wave scattering in a
one-dimensional medium of arbitrary dispersion. It views the wave equation as
an integral equation in Fourier space, which can be solved using standard and
efficient numerical techniques.
