Numerical Spectral Legendre Approach for Solving Space-Time Fractional Advection-Dispersion Problems

Abstract

This manuscript is devoted to implementing spectral numerical solutions to two kinds of fractional space-time advectiondispersion problems governed by certain constraints conditions. The collocation and tau spectral methods are utilized for obtaining the proposed spectral solutions. A double Legendre expansion is proposed as an approximate solution. The main idea of the algorithm is basically depend on converting the equation with its constraints conditions into linear or nonlinear systems of algebraic equations which can be efficiently solved with the aid of suitable numerical solvers. Some illustrative examples are displayed aiming to confirm robustness, efficiency and accuracy of the proposed spectral solutions.