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Stability and convergence of implicit numerical methods for a class of fractional advection-dispersion models

Liu, F., Zhuang, P., & Burrage, K. (2011) Stability and convergence of implicit numerical methods for a class of fractional advection-dispersion models. In Jalili, Nader (Ed.) Proceedings of the ASME 2011 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, ASME, Washington, DC, pp. 85-94.

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Abstract

In this paper, a class of fractional advection-dispersion models (FADM) is investigated. These models include five fractional advection-dispersion models: the immobile, mobile/immobile time FADM with a temporal fractional derivative 0 < γ < 1, the space FADM with skewness, both the time and space FADM and the time fractional advection-diffusion-wave model with damping with index 1 < γ < 2. They describe nonlocal dependence on either time or space, or both, to explain the development of anomalous dispersion. These equations can be used to simulate regional-scale anomalous dispersion with heavy tails, for example, the solute transport in watershed catchments and rivers. We propose computationally effective implicit numerical methods for these FADM. The stability and convergence of the implicit numerical methods are analyzed and compared systematically. Finally, some results are given to demonstrate the effectiveness of our theoretical analysis.

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ID Code: 52822
Item Type: Conference Paper
Keywords: fractional advection-dispersion models
DOI: 10.1115/DETC2011-47071
ISBN: 9780791854808
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2011 ASME
Deposited On: 08 Aug 2012 10:15
Last Modified: 06 Aug 2013 04:50

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