The Impact of Chebyshev Collocation Method on Solutions of fractional Advection–Diffusion Equation

Abstract

The present paper is primarily aimed at obtaining the numerical solution of space fractional advection–diffusion equation including two fractional space derivatives of order. At the first stage, a difference approach with the second-order accuracy is formulated to obtain a semi-discrete scheme. Unconditional stability and convergence analysis has been analyzed. At the second stage, the spatial discretization is accomplished by means of the second kind shifted Chebyshev polynomials. Two examples are investigated, and numerical results are reported to confirm the theoretical results.