Continuous Time Random Walk: Difference between revisions

Jump to navigation Jump to search
Line 62: Line 62:
The main numerical advantage of the FDE approach over the GME is that the FDE allows constructing the final solution in the long-time limit by a single integration,  
The main numerical advantage of the FDE approach over the GME is that the FDE allows constructing the final solution in the long-time limit by a single integration,  
<ref>[http://dx.doi.org/10.1016/j.jcp.2003.07.008 V.E. Lynch et al, ''Numerical methods for the solution of partial differential equations of fractional order'', Journal of Computational Physics '''192''', 2 (2003) 406-421]</ref>
<ref>[http://dx.doi.org/10.1016/j.jcp.2003.07.008 V.E. Lynch et al, ''Numerical methods for the solution of partial differential equations of fractional order'', Journal of Computational Physics '''192''', 2 (2003) 406-421]</ref>
whereas the GME must be iterated in time. On the other hand, the FDE approach does not capture some of the (interesting) dynamical behaviour inherent in the GME approach.
whereas the GME must be iterated in time.  
The FDE approach can be used fruitfully to model transport in fusion plasmas, in finite-size systems.
<ref>[http://link.aip.org/link/?PHPAEN/13/082308/1 D. del-Castillo-Negrete, ''Fractional diffusion models of nonlocal transport'', Phys. Plasmas '''13''' (2006) 082308]</ref>
On the other hand, the FDE approach does not capture some of the (interesting) dynamical behaviour inherent in the GME approach.
<ref>[http://dx.doi.org/10.1088/0029-5515/47/3/004 B.Ph. van Milligen, B.A. Carreras, V.E. Lynch and R. Sánchez, ''Pulse propagation in a simple probabilistic transport model'', Nucl. Fusion '''47''' (2007) 189]</ref>
<ref>[http://dx.doi.org/10.1088/0029-5515/47/3/004 B.Ph. van Milligen, B.A. Carreras, V.E. Lynch and R. Sánchez, ''Pulse propagation in a simple probabilistic transport model'', Nucl. Fusion '''47''' (2007) 189]</ref>


== References ==
== References ==
<references />
<references />

Navigation menu