Gaussian radial basis function and quadrature Sinc method for two-dimensional space-fractional diffusion equations

Abstract

The combination of Sinc quadrature method and double exponential transformation (DE) is a powerful tool to approximate the singular integrals, and radial basis functions (RBFs) are useful for the higher-dimensional space problem. In this study, we develop a numerical method base on Gaussian-RBF combined with QR-factorization of arising matrix and DE-quadrature Sinc method to approximate the solution of two-dimensional space-fractional diffusion equations. When the number of central nodes increases, the ill-conditioning of resultant matrix can be eliminated by using GRBF-QR method. Two numerical examples have been presented to test the efficiency and accuracy of the method.