Monte Carlo evaluation of FADE approach to anomalous kinetics

In this paper we propose a comparison between the CTRW (Monte Carlo) and Fractional Derivative approaches to the modelling of anomalous diffusion phenomena in the presence of an advection field. Galilei variant and invariant schemes are revised.Comment: 13 pages, 6 figure

Some Insights in Superdiffusive Transport

In this paper we deal with high-order corrections for the Fractional Derivative approach to anomalous diffusion, in super-diffusive regime, which become relevand whenever one attempts to describe the behavior of particles close to normal diffusion.Comment: 14 pages, 7 figure

Optimal Collocation Nodes for Fractional Derivative Operators

Spectral discretizations of fractional derivative operators are examined, where the approximation basis is related to the set of Jacobi polynomials. The pseudo-spectral method is implemented by assuming that the grid, used to represent the function to be differentiated, may not be coincident with the collocation grid. The new option opens the way to the analysis of alternative techniques and the search of optimal distributions of collocation nodes, based on the operator to be approximated. Once the initial representation grid has been chosen, indications on how to recover the collocation grid are provided, with the aim of enlarging the dimension of the approximation space. As a results of this process, performances are improved. Applications to fractional type advection-diffusion equations, and comparisons in terms of accuracy and efficiency are made. As shown in the analysis, special choices of the nodes can also suggest tricks to speed up computations