A Spectral Legendre–Gauss–Lobatto Collocation Method for a Space-Fractional Advection Diffusion Equations with Variable Coefficients

An efficient Legendre–Gauss–Lobatto collocation (L–GL–C) method is applied to solve the space-fractional advection diffusion equation with nonhomogeneous initial-boundary conditions. The Legendre–Gauss–Lobatto points are used as collocation nodes for spatial fractional derivatives as well as the Caputo fractional derivative. This approach is reducing the problem to the solution of a system of ordinary differential equations in time which can be solved by using any standard numerical techniques. The proposed numerical solutions when compared with the exact solutions reveal that the obtained solution produces highly accurate results. The results show that the proposed method has high accuracy and is efficient for solving the space-fractional advection diffusion equation.