TY  - EJOU
AU  - Yuan, Xia 
AU  - Jichun, Wu 
AU  - Luying, Zhou 

TI  - Numerical solutions of time-space fractional advection--dispersion equations
T2  - The International Conference on Computational \& Experimental Engineering and Sciences

PY  - 2009
VL  - 9
IS  - 2
SN  - 1933-2815

AB  - This paper establishes a difference approximation on time-space fractional advection-dispersion equations. Based on the difference approximation an ideal numerical example has been solved, and the result is compared with the one of the rigorous time fractional advection-dispersion equation and the rigorous space fractional advection-dispersion equation respectively. The results show: when time fractional order parameter <i>γ</i>=1 or space fractional order parameter <i>α</i>=2, the numerical calculation result of the time-space fractional advection-dispersion equations is in accordance with that of the rigorous time fractional advection-dispersion equation or the rigorous space fractional advection-dispersion equation. The variation law of the result with parameter is also similar to them, that is when <i>γ</i> is smaller, diffusion is slower; when <i>α</i> is smaller, diffusion is faster. The simulation calculation for a practical example indicates that time-space fractional advection-dispersion equations can simulate the skewness and the tail of anomalous diffusion. This paper provides a efficient tool for the research of fractional advection-dispersion equations.
KW  - fractional advection-dispersion equation
KW  -  anomalous diffusion
KW  -  time-space relativity
KW  -  numerical solution

DO  - 10.3970/icces.2009.009.117