A New Numerical Algorithm for Solving a Class of Fractional Advection-Dispersion Equation with Variable Coefficients Using Jacobi Polynomials

Abstract

We propose Jacobi-Gauss-Lobatto collocation approximation for the numerical solution of a class of fractional-in-space advection-dispersion equation with variable coefficients based on Caputo derivative. This approach has the advantage of transforming the problem into the solution of a system of ordinary differential equations in time this system is approximated through an implicit iterative method. In addition, some of the known spectral collocation approximations can be derived as special cases from our algorithm if we suitably choose the corresponding special cases of Jacobi parameters $\alpha$ and $\beta$. Finally, numerical results are provided to demonstrate the effectiveness of the proposed spectral algorithms.