@Article{icces.2009.009.117,
AUTHOR = {Xia Yuan, Wu Jichun, Zhou Luying},
TITLE = {Numerical solutions of time-space fractional advection--dispersion equations},
JOURNAL = {The International Conference on Computational \& Experimental Engineering and Sciences},
VOLUME = {9},
YEAR = {2009},
NUMBER = {2},
PAGES = {117--126},
URL = {http://www.techscience.com/icces/v9n2/30144},
ISSN = {1933-2815},
ABSTRACT = {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.},
DOI = {10.3970/icces.2009.009.117}
}