  A new approach is presented for the solution of spectral problems on infinite
domains with regular ends, which avoids the need to solve boundary value
problems for many trial values of the spectral parameter. We present numerical
results both for eigenvalues and for resonances, comparing with results
reported by Aslanyan, Parnovski and Vassiliev [{\em Q. J. Mech. Appl. Math.}
{\bfseries 53} (2000), 429--447].
