Explicit finite difference methods for the solution of the one dimensional time fractional advection-diffusion equation

Abstract

In this paper, two explicit finite difference methods are developed to solve one dimensional time fractional advection-diffusion equation with boundary values which are functions. The fractional derivative is treated by applying shifted Grünwald-Letnikov formula of order α ∈(0,1) while the first and second order spatial derivatives are replaced by the corresponding finite difference approximations. The stability analysis is investigated via von Neumann method. Numerical results are presented to demonstrate the effectiveness of the schemes.