A Numerical Algorithm for the Caputo Tempered Fractional Advection-Diffusion Equation

Abstract

By transforming the Caputo tempered fractional advection-diffusion equation into the Riemann–Liouville tempered fractional advection-diffusion equation, and then using the fractional-compact Grünwald–Letnikov tempered difference operator to approximate the Riemann–Liouville tempered fractional partial derivative, the fractional central difference operator to discritize the space Riesz fractional partial derivative, and the classical central difference formula to discretize the advection term, a numerical algorithm is constructed for solving the Caputo tempered fractional advection-diffusion equation. The stability and the convergence analysis of the numerical method are given. Numerical experiments show that the numerical method is effective.