Finite Point Method for the Time Fractional Convection-Diffusion Equation

Abstract

The paper presents a meshless finite point method for solving one-dimensional and two-dimensional time fractional convection-diffusion equations. The method is based on the combination of the moving least square shape function with the collocation method. Moreover, the process of forcing the stable term can effectively solve the convection dominant problem. The Caputo time fractional derivative is discretized by an approximation formula based on L1 interpolation. Furthermore, the stability related to the discretization of this approach is theoretically proven. At the same time, numerical examples are given to compare the errors of the proposed method and the L1 approximation finite difference method. The numerical results show that the proposed method has high accuracy and can effectively eliminate the oscillations.