Due to their capability to reduce turbulent transport in magnetized plasmas,
understanding the dynamics of zonal flows is an important problem in the fusion
programme. Since the pioneering work by Rosenbluth and Hinton in axisymmetric
tokamaks, it is known that studying the linear and collisionless relaxation of
zonal flow perturbations gives valuable information and physical insight.
Recently, the problem has been investigated in stellarators and it has been
found that in these devices the relaxation process exhibits a characteristic
feature: a damped oscillation. The frequency of this oscillation might be a
relevant parameter in the regulation of turbulent transport, and therefore its
efficient and accurate calculation is important. Although an analytical
expression can be derived for the frequency, its numerical evaluation is not
simple and has not been exploited systematically so far. Here, a numerical
method for its evaluation is considered, and the results are compared with
those obtained by calculating the frequency from gyrokinetic simulations. This
"semianalytical" approach for the determination of the zonal-flow frequency
reveals accurate and faster than the one based on gyrokinetic simulations.