Numerical methods and analysis for a class of fractional advection dispersion models
In this paper, 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 < γ < 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 < γ < 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.
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|Item Type:||Journal Article|
|Keywords:||Fractional advection–dispersion models, Implicit numerical methods, Stability, Convergence, Fractional calculus|
|Subjects:||Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000)|
|Divisions:||Current > Schools > School of Mathematical Sciences|
Current > QUT Faculties and Divisions > Science & Engineering Faculty
|Copyright Owner:||Copyright 2012 Elsevier Ltd.|
|Deposited On:||10 Jul 2012 13:21|
|Last Modified:||16 May 2013 12:43|
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