This paper aims to employ the implicit radial point interpolation method, which is intrinsically meshless, for the numerical simulation of nonlinear space fractional advection-diffusion equations. The space fractional derivative is defined in the Caputo sense and calculated by the Gauss’s Jacobi quadrature formula. The accuracy and convergency of the proposed meshless method are demonstrated by several numerical examples with different regions and different nodal distributions. It is proved that the presented method is computational efficiency for modeling and simulation of nonlinear SFADEs.
"Implicit radial point interpolation method for nonlinear space fractional advection-diffusion equations." Rocky Mountain J. Math. 50 (6) 2199 - 2212, December 2020. https://doi.org/10.1216/rmj.2020.50.2199