NUMERICAL APPROXIMATION OF THE SMOLUCHOWSKI EQUATION USING RADIAL BASIS FUNCTIONS

• 来源期刊: 计算数学（英文版）
• 关键词: Smoluchowski equation Spectral method Radial basis function method
• 年，卷（期）: 2020,（1）
• 页码范围: 176-194
• 页数: 19页
• 语种: 英文
• DOI: 10.4208/jcm.1908-m2018-0211

摘要

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 alternative for these kind of models.