作者
Fawang Liu, Pinghui Zhuang, Ian Turner, Kevin Burrage, Vo Anh
发表日期
2014/8/1
期刊
Applied Mathematical Modelling
卷号
38
期号
15-16
页码范围
3871-3878
出版商
Elsevier
简介
The inherent heterogeneities of many geophysical systems often gives rise to fast and slow pathways to water and chemical movement. One approach to model solute transport through such media is by fractional diffusion equations with a space–time dependent variable coefficient. In this paper, a two-sided space fractional diffusion model with a space–time dependent variable coefficient and a nonlinear source term subject to zero Dirichlet boundary conditions is considered.
Some finite volume methods to solve a fractional differential equation with a constant dispersion coefficient have been proposed. The spatial discretisation employs fractionally-shifted Grünwald formulas to discretise the Riemann–Liouville fractional derivatives at control volume faces in terms of function values at the nodes. However, these finite volume methods have not been extended to two-dimensional and three-dimensional problems in a …
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F Liu, P Zhuang, I Turner, K Burrage, V Anh - Applied Mathematical Modelling, 2014