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Continuous Time Random Walk: Difference between revisions
→Fractional Differential Equations
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If nothing else, this serves to show that all of the above constitute generalizations (on various levels) of the usual transport equations. | If nothing else, this serves to show that all of the above constitute generalizations (on various levels) of the usual transport equations. | ||
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, whereas the GME must be iterated in time. On the other hand, the FDE approach does not capture the (interesting) dynamical behaviour inherent in the GME approach. | 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> | |||
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. | |||
<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 /> | ||