Numerical methods and analysis for a class of fractional advection-dispersion models. (English) Zbl 1268.65124

Liu, F.; Zhuang, P.; Burrage, K.

Comput. Math. Appl. 64, No. 10, 2990-3007 (2012).

Summary: A class of fractional advection-dispersion models (FADMs) is considered. These models include five fractional advection-dispersion models, i.e., the time FADM, the mobile/immobile time FADM with a time Caputo fractional derivative \(0<\gamma<1\), the space FADM with two sides Riemann-Liouville derivatives, the time-space FADM and the time fractional advection-diffusion-wave model with damping with index \(1<\gamma<2\). These equations can be used to simulate the regional-scale anomalous dispersion with heavy tails. We propose computationally effective implicit numerical methods for these FADMs. The stability and convergence of the implicit numerical methods are analysed and compared systematically. Finally, some results are given to demonstrate the effectiveness of theoretical analysis.

MSC:

65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35R11	Fractional partial differential equations
45K05	Integro-partial differential equations

Keywords:

fractional advection; dispersion models; implicit numerical methods; stability; convergence; fractional calculus

Software:

ma2dfc

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