The goal of this paper is to present a numerical method for the Smoluchowski equation,a drift-diffusion equation on the sphere,arising in the modelling of particle dynamics.The numerical method uses radial basis functions (RBF).This is a relatively new approach,which has recently mainly been used for geophysical applications.For a simplified model problem we compare the RBF approach with a spectral method,i.e.the standard approach used in related physical applications.This comparison as well as our other accuracy studies show that RBF methods are an attractive alteative for these kind of models.