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	Numerical simulation technique for fractional-order equation in fractal media
	Cai, X ; Liu, FW ; Liu FW(刘发旺)
	2006-12
关键词	SYSTEMS
英文摘要	The fractional-order equation was obtained from the standard equation by replacing the derivative with a fractional order. It has been used to many relevant physical processes such as chaos, control system, kinetic theory. In the fractal features of a process or the medium impose a necessity of applying tools that are non-traditional in "regular" smooth physical equations, the new type of problem has rapidly increased studied. Wave propagation in media with fractal properties was considered. Firstly, the fractional Ginzbyrg-Landau equation was generalized. The physical structure of the problem was commented. Since the analytic solution was so difficult to solve, this motives us to consider the simulation technique. Secondly, the fractional Ginzbyrg-Landau equation may be transferred to a system. The existence and uniqueness of the new system are proved. Thirdly, a fractional order difference approximation was constructed. The consistence, convergence and stability of numerical method are proved. Finally, the simulation results are presented to demonstrate that the novel method is a computationally efficient method. The new technique can be applied to solve the similar problem in fractal media.
语种	英语
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/66107]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Cai, X,Liu, FW,Liu FW. Numerical simulation technique for fractional-order equation in fractal media[J],2006.
APA	Cai, X,Liu, FW,&刘发旺.(2006).Numerical simulation technique for fractional-order equation in fractal media..
MLA	Cai, X,et al."Numerical simulation technique for fractional-order equation in fractal media".(2006).

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