An advanced meshless method for time fractional diffusion equation

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	An advanced meshless method for time fractional diffusion equation
	Gu, Y.T. ; Zhuang, P. ; Liu, Q. ; Liu Q(刘青)
刊名	http://dx.doi.org/10.1142/S0219876211002745
	2011
关键词	Computer simulation Differentiation (calculus) Finite difference method Partial differential equations
英文摘要	Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modeling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is finite difference method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate 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 FPDEs. ? 2011 World Scientific Publishing Company.
语种	英语
出版者	World Scientific Publishing Co. Pte. Ltd
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/91438]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Gu, Y.T.,Zhuang, P.,Liu, Q.,et al. An advanced meshless method for time fractional diffusion equation[J]. http://dx.doi.org/10.1142/S0219876211002745,2011.
APA	Gu, Y.T.,Zhuang, P.,Liu, Q.,&刘青.(2011).An advanced meshless method for time fractional diffusion equation.http://dx.doi.org/10.1142/S0219876211002745.
MLA	Gu, Y.T.,et al."An advanced meshless method for time fractional diffusion equation".http://dx.doi.org/10.1142/S0219876211002745 (2011).