In this paper we study the diffusion approximation of a swarming model given by a system
of interacting Langevin equations with nonlinear friction. The diffusion approximation
requires the calculation of the drift and diffusion coefficients that are given as averages of
solutions to appropriate Poisson equations. We present a new numerical method for computing
these coefficients that is based on the calculation of the eigenvalues and eigenfunctions
of a Schr¨odinger operator. These theoretical results are supported by numerical simulations
showcasing the efficiency of the method.