Particle Based gPC Methods for Mean-Field Models of Swarming with Uncertainty (Communications in Computational Physics, 2018)
In this work we focus on the construction of numerical schemes for the approximationof stochastic mean-field equations which preserve the nonnegativity ofthe solution. The method here developed makes use of a mean-field Monte Carlomethod in the physical variables combined with a generalized Polynomial Chaos (gPC)expansion in the random space. In contrast to a direct application of stochastic-Galerkinmethods, which are highly accurate but lead to the loss of positivity, the proposedschemes are capable to achieve high accuracy in the random space without loosingnonnegativity of the solution. Several applications of the schemes to mean-field modelsof collective behavior are reported.