Least-Squares Spectral Method for the solution of a fractional advectiondispersion equation
Fractional derivatives provide a general approach for modeling transport phenomena occurring in diverse fields. This article describes a Least Squares Spectral Method for solving advectiondispersion equations using Caputo or RiemannLiouville fractional derivatives. A GaussLobattoJacobi quadrature is implemented to approximate the singularities in the integrands arising from the fractional derivative definition. Exponential convergence rate of the operator is verified when increasing the order of the approximation. Solutions are calculated for fractional-time and fractional-space differential equations. Comparisons with finite difference schemes are included. A significant reduction in storage space is achieved by lowering the resolution requirements in the time coordinate.
least-squares spectral method advectiondispersion fractional derivative caputo derivative riemannliouville derivative riesz derivative anomalous diffusion anomalous transport