Second Kind Chebyshev Polynomials for Solving Space Fractional Advection–Dispersion Equation Using Collocation Method

Abstract

Fractional space derivatives are studied for modeling anomalous diffusion or dispersion, where a particle plume spreads at a rate inconsistent with the classical Brownian motion model. In this paper, we discuss numerical technique for solving space fractional advection–dispersion equation (FADE) where $$1<\alpha \leq 2$$ and $$0<\beta \leq 1$$ . We implement a numerical technique for solving FADE called Chebyshev collocation method. We utilized fractional derivatives in the Caputo sense. The properties of shifted Chebyshev polynomials of second kind (SCPSK) are used to reduce FADE to a system of differential equations (ODEs), which is solved by finite difference method (FDM), then we use an iteration scheme to solve the system of equations. Specially, we are focused on error analysis and convergence analysis of the proposed method. The validation of the present scheme is tested through examples and compare with existing method and exact solution.