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	Numerical approximations and solution techniques for the space-time Riesz-Caputo fractional advection-diffusion equation
	Shen, S. J. ; Liu, F. W. ; Anh, V. ; Liu FW(刘发旺)
	2011
关键词	: Numerical approximation Riesz fractional derivative Caputo fractional derivative Stability and convergence Richardson extrapolation Short-memory principle
英文摘要	In this paper, we consider a space-time Riesz-Caputo fractional advection-diffusion equation. The equation is obtained from the standard advection-diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative of order alpha is an element of (0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of order beta(1) is an element of (0,1) and beta(2) is an element of (1,2], respectively. We present an explicit difference approximation and an implicit difference approximation for the equation with initial and boundary conditions in a finite domain. Using mathematical induction, we prove that the implicit difference approximation is unconditionally stable and convergent, but the explicit difference approximation is conditionally stable and convergent. We also present two solution techniques: a Richardson extrapolation method is used to obtain higher order accuracy and the short-memory principle is used to investigate the effect of the amount of computations. A numerical example is given; the numerical results are in good agreement with theoretical analysis.
语种	英语
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/66100]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Shen, S. J.,Liu, F. W.,Anh, V.,et al. Numerical approximations and solution techniques for the space-time Riesz-Caputo fractional advection-diffusion equation[J],2011.
APA	Shen, S. J.,Liu, F. W.,Anh, V.,&刘发旺.(2011).Numerical approximations and solution techniques for the space-time Riesz-Caputo fractional advection-diffusion equation..
MLA	Shen, S. J.,et al."Numerical approximations and solution techniques for the space-time Riesz-Caputo fractional advection-diffusion equation".(2011).

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