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A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions
- Source :
- Advances in Mathematical Physics, Vol 2017 (2017)
- Publication Year :
- 2017
- Publisher :
- Hindawi, 2017.
-
Abstract
- Fractional advection-dispersion equations, as generalizations of classical integer-order advection-dispersion equations, are used to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper, we develop an implicit finite difference method for fractional advection-dispersion equations with fractional derivative boundary conditions. First-order consistency, solvability, unconditional stability, and first-order convergence of the method are proven. Then, we present a fast iterative method for the implicit finite difference scheme, which only requires storage of O(K) and computational cost of O(Klogā”K). Traditionally, the Gaussian elimination method requires storage of O(K2) and computational cost of O(K3). Finally, the accuracy and efficiency of the method are checked with a numerical example.
- Subjects :
- Article Subject
Iterative method
Physics
QC1-999
Applied Mathematics
Mathematical analysis
Finite difference method
General Physics and Astronomy
010103 numerical & computational mathematics
01 natural sciences
Stability (probability)
Fractional calculus
010101 applied mathematics
symbols.namesake
Gaussian elimination
Convergence (routing)
symbols
Fluid dynamics
Boundary value problem
0101 mathematics
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 16879120
- Database :
- OpenAIRE
- Journal :
- Advances in Mathematical Physics
- Accession number :
- edsair.doi.dedup.....0466a553cdbd640ecb58a0e1836dc4ed
- Full Text :
- https://doi.org/10.1155/2017/8716752