Stability and convergence of a finite volume method for the space fractional advection-dispersion equation
Data(s) |
07/10/2014
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Resumo |
We consider the space fractional advection–dispersion equation, which is obtained from the classical advection–diffusion equation by replacing the spatial derivatives with a generalised derivative of fractional order. We derive a finite volume method that utilises fractionally-shifted Grünwald formulae for the discretisation of the fractional derivative, to numerically solve the equation on a finite domain with homogeneous Dirichlet boundary conditions. We prove that the method is stable and convergent when coupled with an implicit timestepping strategy. Results of numerical experiments are presented that support the theoretical analysis. |
Formato |
application/pdf |
Identificador | |
Publicador |
Elsevier BV |
Relação |
http://eprints.qut.edu.au/56974/1/Hala_paper1_Y11m10d6.pdf DOI:10.1016/j.cam.2013.06.039 Hejazi, Hala, Moroney, Timothy J., & Liu, Fawang (2014) Stability and convergence of a finite volume method for the space fractional advection-dispersion equation. Journal of Computational and Applied Mathematics, 255, pp. 684-697. |
Direitos |
Copyright 2012 Elsevier BV This is the author’s version of a work that was accepted for publication in Journal of Computational and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational and Applied Mathematics, [VOL 255, (2014)] DOI: 10.1016/j.cam.2013.06.039 |
Fonte |
School of Mathematical Sciences; Science & Engineering Faculty |
Palavras-Chave | #010301 Numerical Analysis #010399 Numerical and Computational Mathematics not elsewhere classified #Fractional advection-dispersion #finite volume method #shifted Grunwald #stability #convergence |
Tipo |
Journal Article |