A Novel Algorithm for Time Fractional Advection-Diffusion Equation

The purpose of this paper is to design a discrete-continuous coupled numerical algorithm for solving a time fractional advection-diffusion equation. Firstly, we discretize time variable by linear interpolation to obtain differential equations about spatial variable. Secondly, numerical algorithm is designed to solve the above differential equations using Legendre wavelet basis constructed in the reproducing kernel space W-2(3)[0,1]. Therefore, the numerical solution of the time fractional advection-diffusion equation is obtained. Furthermore, the convergence analysis and stability analysis of the proposed algorithm have been provided. Finally, five numerical examples are proposed respectively to verify the correctness of our theoretical analysis and to demonstrate the validity and applicability of the technique.