Efficient numerical calculation of drift and diffusion coefficients in the diffusion approximation of kinetic equations
For researchers modeling swarming behavior via kinetic equations, this method offers a more efficient way to compute key coefficients, though it is domain-specific and incremental.
The authors present a new numerical method for computing drift and diffusion coefficients in the diffusion approximation of kinetic equations, using eigenvalues and eigenfunctions of a Schrödinger operator. Numerical simulations demonstrate its efficiency.
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 Schrödinger operator. These theoretical results are supported by numerical simulations showcasing the efficiency of the method.