Numerical solutions of time-space fractional advection-dispersion equations

Summary This paper establishes a difference approximation on time-space fractional advectiondispersion 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 γ=1 or space fractional order parameter α=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 γ is smaller, diffusion is slower; when α 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