Fourth Kind Shifted Chebyshev Polynomials for Solving Space Fractional Order Advection–Dispersion Equation Based on Collocation Method and Finite Difference Approximation

Abstract

In this paper, we study the numerical solution of one-dimensional space fractional advection–dispersion equations (FADE). The integer order space derivatives are replaced by fractional derivatives in the Caputo sense. The proposed scheme is based on the collocation method and the finite difference method (FDM). An effective method is applied for solving FADE by using the shifted Chebyshev polynomials of fourth kind (SCPFK) to reduce FADE to a system of ordinary differential equations, which can be solved by FDM, then apply an iteration method to solve this system of equations. This method is unconditionally stable, consistent and convergent. Also we are discussed about error analysis, convergence and error bound. The efficiency of the proposed method is tested through number of examples and compared with previous work in the literature for this we needed small number of SCPFK.