Time-dependent fractional advection-diffusion equations by an implicit MLS meshless method

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	Time-dependent fractional advection-diffusion equations by an implicit MLS meshless method
	Zhuang, P. ; Gu, Y. T. ; Liu, F. ; Turner, I. ; Yarlagadda, P. K. D. V. ; Zhuang PH(庄平辉)
刊名	http://dx.doi.org/10.1002/nme.3223
	2011-12-30
关键词	POINT INTERPOLATION METHOD PETROV-GALERKIN MLPG COMPUTATIONAL MECHANICS DISPERSION EQUATION ANOMALOUS DIFFUSION STRUCTURAL-ANALYSES APPROXIMATION TRANSPORT DYNAMICS FORMULATION
英文摘要	ARC [FT100100172]; NSF of Fujian [2010J01011]; Recently, many new applications in engineering and science are governed by a series of fractional partial differential equations (FPDEs). Unlike the normal partial differential equations (PDEs), the differential order in an FPDE is with a fractional order, which will lead to new challenges for numerical simulation, because most existing numerical simulation techniques are developed for the PDE with an integer differential order. The current dominant numerical method for FPDEs is finite difference method (FDM), which is usually difficult to handle a complex problem domain, and also difficult to use irregular nodal distribution. This paper aims to develop an implicit meshless approach based on the moving least squares (MLS) approximation for numerical simulation of fractional advectiondiffusion equations (FADE), which is a typical FPDE The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless strong-forms. The stability and convergence related to the time discretization of this approach are then discussed and theoretically proven. Several numerical examples with different problem domains and different nodal distributions are used to validate and investigate the accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the FADE. Copyright (C) 2011 John Wiley & Sons, Ltd.
语种	英语
出版者	INT J NUMER METH ENG
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/91060]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Zhuang, P.,Gu, Y. T.,Liu, F.,et al. Time-dependent fractional advection-diffusion equations by an implicit MLS meshless method[J]. http://dx.doi.org/10.1002/nme.3223,2011.
APA	Zhuang, P.,Gu, Y. T.,Liu, F.,Turner, I.,Yarlagadda, P. K. D. V.,&庄平辉.(2011).Time-dependent fractional advection-diffusion equations by an implicit MLS meshless method.http://dx.doi.org/10.1002/nme.3223.
MLA	Zhuang, P.,et al."Time-dependent fractional advection-diffusion equations by an implicit MLS meshless method".http://dx.doi.org/10.1002/nme.3223 (2011).