TY - JOUR
T1 - Numerical Approximation of the Smoluchowski Equation Using Radial Basis Functions
AU - Helzel , Christiane
AU - Schneiders , Maximilian
JO - Journal of Computational Mathematics
VL - 1
SP - 176
EP - 194
PY - 2020
DA - 2020/02
SN - 38
DO - http://doi.org/10.4208/jcm.1908-m2018-0211
UR - https://global-sci.org/intro/article_detail/jcm/13690.html
KW - Smoluchowski equation, Spectral method, Radial basis function method.
AB - <p style="text-align: justify;"><span style="font-size: 20px;">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 shows that RBF methods are an attractive alternative for this kind of models.</span></p>