A fast semi-discrete Kansa method to solve the two-dimensional   spatiotemporal fractional diffusion
  Anomalous diffusion is a common phenomenon observed in underground solute transport, soil water infiltration and sediment movement, etc. Time and space fractional derivative advection-dispersion equation (FADE) has been widely employed as the governing equation to characterize above mentioned anomalous diffusion related processes. However, a main problem in application of time and space FADE model to describe the real-world mass transport processes, is its low computation efficiency for long-time range and large irregular domain cases. This study offers a new algorithm in which the Kansa method is used for vector space fractional derivative term discretization and then analytical approach for resulted time fractional ordinary system. The influence of node distribution mode and node numbers on accuracy and convergence rate are analysed through the numerical examples in one and two dimensional cases. To test the application potentials of present methods, we offer the numerical results of two dimensional time and space FADE models in continuous and discrete cases. It shows that the solute plumes in heterogeneous and anisotropic media, can be well simulated by using present method compared with the previous time-consumed particle Monte-Carlo methods. 
HongGuang Sun, Xiaoting Liu, Yong Zhang, Guofei Pang, Rhiannon Garrard
math.NA