Numerical analysis of a new space-time variable fractional order advection-dispersion equation

Zhang, H., Liu, Fawang, Zhuang, Pinghui, Turner, Ian, & Anh, Vo (2014) Numerical analysis of a new space-time variable fractional order advection-dispersion equation. Applied Mathematics and Computation, 242, pp. 541-550.

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Many physical processes appear to exhibit fractional order behavior that may vary with time and/or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider a new space–time variable fractional order advection–dispersion equation on a finite domain. The equation is obtained from the standard advection–dispersion equation by replacing the first-order time derivative by Coimbra’s variable fractional derivative of order α(x)∈(0,1]α(x)∈(0,1], and the first-order and second-order space derivatives by the Riemann–Liouville derivatives of order γ(x,t)∈(0,1]γ(x,t)∈(0,1] and β(x,t)∈(1,2]β(x,t)∈(1,2], respectively. We propose an implicit Euler approximation for the equation and investigate the stability and convergence of the approximation. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

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14 citations in Scopus
17 citations in Web of Science®
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ID Code: 88767
Item Type: Journal Article
Refereed: Yes
Keywords: Variable fractional derivative, Advection–dispersion equation, Implicit Euler scheme, Stability, Convergence
DOI: 10.1016/j.amc.2014.06.003
ISSN: 0096-3003
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2014 Elsevier Inc
Deposited On: 29 Oct 2015 05:24
Last Modified: 29 Oct 2015 05:24

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