  We propose a family of compactly supported parametric interaction functions
in the general Cucker-Smale flocking dynamics such that the mean-field
macroscopic system of mass and momentum balance equations with non-local
damping terms can be converted from a system of partial integro-differential
equations to an augmented system of partial differential equations in a compact
set. We treat the interaction functions as Green's functions for an operator
corresponding to a semi-linear Poisson equation and compute the density and
momentum in a translating reference frame, i.e. one that is taken in reference
to the flock's centroid. This allows us to consider the dynamics in a fixed,
flock-centered compact set without loss of generality. We approach the
computation of the non-local damping using the standard finite difference
treatment of the chosen differential operator, resulting in a tridiagonal
system which can be solved quickly.
