Numerical approximations for the Riesz space fractional advection-dispersion equations via radial basis functions

The radial basis functions collocation method is developed to solve Riesz space fractional advection-dispersion equation (RSFADE). To do this, we first provide the Riemann-Liouville fractional derivatives of the five kinds of RBFs, including the Powers, Gaussian, Multiquadric, Matern and Thin-plate splines, in one dimension. Then a method of lines, implemented as a meshless method based on spatial trial spaces spanned by the RBFs is developed for the numerical solution of the RSFADE. Numerical experiments are presented to validate the newly developed method and to investigate accuracy and efficiency. The numerical rate of convergence in space is computed. The stability of the linear systems arising from discretizing the Riesz fractional derivative with RBFs is also analysed. (C) 2019 !MACS. Published by Elsevier B.V. All rights reserved.