Semi-discretized numerical solution for time fractional convection–diffusion equation by RBF-FD

Abstract

In this paper, a numerical method based on radial basis functions finite difference (RBF-FD) has been developed for solving the time fractional convection–diffusion equation. We first approximate the time fractional derivative by FD and obtain the semi-discretized scheme. The unconditional stability and convergence of the semi-discretized scheme are given. After that, we use the multiquadric RBF to approximate the spatial derivatives in the numerical experiments. The aim of this paper is to show that the RBF-FD method is better than the classical FD method for solving our mentioned equation. Finally, two numerical examples are proposed respectively to verify the correctness of our theoretical analysis and to demonstrate the superiority of the RBF-FD method.