FINITE DIFFERENCE/SPECTRAL APPROXIMATIONS FOR THE FRACTIONAL CABLE EQUATION

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	FINITE DIFFERENCE/SPECTRAL APPROXIMATIONS FOR THE FRACTIONAL CABLE EQUATION
	Lin, Yumin ; Li, Xianjuan ; Xu, Chuanju ; Xu CJ(许传炬)
刊名	http://dx.doi.org/10.1090/S0025-5718-2010-02438-X
	2011-07
关键词	FOKKER-PLANCK EQUATION SINGLE-MOLECULE TRACKING TIME RANDOM-WALKS ANOMALOUS DIFFUSION PLASMA-MEMBRANE TRANSPORT DISPERSION SPACE MEDIA MODEL
英文摘要	Fujian NSF [S0750017]; National NSF of China [10531080]; Ministry of Education of China; 973 High Performance Scientific Computation Research Program [2005CB321703]; The Cable equation has been one of the most fundamental equations for modeling neuronal dynamics. In this paper, we consider the numerical solution of the fractional Cable equation, which is a generalization of the classical Cable equation by taking into account the anomalous diffusion in the movement of the ions in neuronal system. A schema combining a finite difference approach ill the time direction and a spectral method in the space direction is proposed and analyzed. The main contribution of this work is threefold: 1) We construct a finite difference/Legendre spectral schema for discretization of the fractional Cable equation. 2) We give a detailed analysis of the proposed schema by providing some stability and error estimates. Based on this analysis, the convergence of the method is rigourously established. We prove that the overall schema is unconditionally stable, and the numerical solution converges to the exact one with order O(Delta t(2-max{alpha,beta})+ Delta t(-1)N(-m)), where Delta t, N and m are respectively the time step size, polynomial degree, and regularity in the space variable of the exact solution, alpha and beta are two different exponents between 0 and 1 involved in the fractional derivatives. 3) Finally, some numerical experiments are carried out to support the theoretical claims.
语种	英语
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/66582]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Lin, Yumin,Li, Xianjuan,Xu, Chuanju,et al. FINITE DIFFERENCE/SPECTRAL APPROXIMATIONS FOR THE FRACTIONAL CABLE EQUATION[J]. http://dx.doi.org/10.1090/S0025-5718-2010-02438-X,2011.
APA	Lin, Yumin,Li, Xianjuan,Xu, Chuanju,&许传炬.(2011).FINITE DIFFERENCE/SPECTRAL APPROXIMATIONS FOR THE FRACTIONAL CABLE EQUATION.http://dx.doi.org/10.1090/S0025-5718-2010-02438-X.
MLA	Lin, Yumin,et al."FINITE DIFFERENCE/SPECTRAL APPROXIMATIONS FOR THE FRACTIONAL CABLE EQUATION".http://dx.doi.org/10.1090/S0025-5718-2010-02438-X (2011).