A numerical scheme for space-time fractional advection-dispersion equation

In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. The main idea of the present method is that we utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives and it leads to a simple evaluation of the related terms. By using the Bernstein polynomial approximation, the problem is transformed into a linear system of algebraic equations. The error analysis and the order of convergence of the proposed algorithm are also discussed. Some numerical experiments are presented to demonstrate the effectiveness of the proposed method and to conrm the analytic results.