A finite volume method for two-sided fractional diffusion equations on non-uniform meshes
type: Item
instance of: scholarly article
title: A finite volume method for two-sided fractional diffusion equations on non-uniform meshes
zbMATH Open document ID: 1383.65101
author: Alex Simmons
author: Qianqian Yang
author: Timothy J. Moroney
published in: Journal of Computational Physics
publication date: 2017-12-14T00:00:00Z
full work available at URL: Revision2.pdf
review text: The authors derive a new finite volume scheme for two-sided fractional diffusion equations with Riemann-Liouville derivatives in one spatial dimension. Spatial mesh is non-uniform. The discretisation uses the integral definition of the fractional derivatives. The scheme leads to a diagonally dominant matrix representation and it is proved to be stable and fully conservative. Some numerical examples are presented to justify that the scheme is more accurate for the same number of nodes compared to a uniform mesh.
reviewed by: Abdallah Bradji
Mathematics Subject Classification ID: 65M08
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 65M50
Mathematics Subject Classification ID: 65M12
zbMATH DE Number: 6818418
zbMATH Keywords: fractional diffusion equation
zbMATH Keywords: Riemann-Liouville fractional derivative
zbMATH Keywords: finite volume method
zbMATH Keywords: non-uniform mesh
zbMATH Keywords: diagonally dominant matrix representation
zbMATH Keywords: stability
zbMATH Keywords: numerical examples
describes a project that uses: quadgk
describes a project that uses: quadva
MaRDI profile type: Publication
OpenAlex ID: W2586768575
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DOI: 10.1016/J.JCP.2017.01.061
description: scientific article; zbMATH DE number 6818418