Numerical solution of the space-time fractional diffusion equation: Alternatives to finite differences

摘要：

One of the ongoing issues with fractional-order diffusion models is the design of efficient numerical schemes for the space and time discretizations. Until now, most models have relied on a low-order finite difference method to discretize both the fractional-order space and time derivatives. While the finite difference method is simple and straightforward to solve integer-order differential equations, its appeal is reduced for fractional-order differential equations as it leads to systems of linear equation defined by large full matrices. Alternatives to the finite difference method exist but a unified presentation and comparison of these methods is still missing. In this paper, we compare 4 different numerical discretizations of the space-time fractional diffusion model. These consist of the finite difference, finite element, pseudo-spectral and radial basis functions methods. We suggest that non-local methods, like the pseudo-spectral and radial basis functions method, are well-suited to discretize the non-local operators like fractional-order derivatives. These methods naturally take the global behavior of the solution into account and thus do not result in an extra computational cost when moving from an integer-order to a fractional-order diffusion model.

关键词： Space-time fractional diffusion equation finite difference finite element pseudo-spectral and radial basis functions method Mittag-Leffler functions

作者: Emmanuel Hanert Cécile Piret

作者单位: Earth and Life Institute, Universite catholique de Louvain, 1348Louvain-la-Neuve, Belgium Institute of Mechanics, Materials and Civil Engineering, Universite catholique de Louvain, 1348 Lou

会议类型: 国际会议

会议名称: The Fifth Symposium on Fractional Differentiation and Its Applications(第五届国际自动控制联合会分数阶导数及其应用会议)

会议地点: 南京

会议语种:英文

页码: 1-8

在线出版日期: 2012-05-14（万方平台首次上网日期，不代表论文的发表时间）