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.
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.
Impact and interest:
Citation counts are sourced monthly from and citation databases.
These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.
Citations counts from theindexing service can be viewed at the linked Google Scholar™ search.
|Item Type:||Journal Article|
|Keywords:||Variable fractional derivative, Advection–dispersion equation, Implicit Euler scheme, Stability, Convergence|
|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|
Repository Staff Only: item control page