  A measurement of the neutrino mass scale will be achieved with cosmological
probes in the upcoming decade. On one hand, the inclusion of massive neutrinos
in the linear perturbation theory of cosmological structure formation is well
understood and can be done accurately with state of the art Boltzmann solvers.
On the other hand, the numerical implementation of the Boltzmann equation is
computationally expensive and is a bottleneck in those codes. This has
motivated the development of more efficient fluid approximations, despite their
limited accuracy over all scales of interest, $k \sim (10^{-3}-10)$Mpc$^{-1}$.
In this work we account for the dispersive nature of the neutrino fluid, i.e.,
the scale dependence in the sound speed, leading to an improved fluid
approximation. We show that overall $\lesssim 5\%$ errors can be achieved for
the neutrino density and velocity transfer functions at redshift $z \lesssim
5$, which corresponds to an order of magnitude improvement over previous
approximation schemes that can be discrepant by as much as a factor of two.
