Sturm-Liouville problem and numerical method of fractional diffusion equation on fractals

CORC > 武汉物理与数学研究所 > 中国科学院武汉物理与数学研究所 > 数学物理与应用研究部

	Sturm-Liouville problem and numerical method of fractional diffusion equation on fractals
	Zhang, Wenbiao 1; Yi, Ming 2
刊名	ADVANCES IN DIFFERENCE EQUATIONS
	2016-08-25
关键词	fractional diffusion equation anomalous diffusion Sturm-Liouville problem implicit numerical scheme robustness
英文摘要	Classical diffusion theory is widely applied in natural science and has made a great achievement. However, the phenomenon of anomalous diffusion in discontinuous media (fractal, porous, etc.) shows that classical diffusion theory is no longer suitable. The differential equations with fractional order have recently been proved to be powerful tools for describing anomalous diffusion. Nevertheless, the analysis methods and numerical methods for fractional differential equations are still in the stage of exploration. In the paper, we consider the Sturm-Liouville problem and the numerical method of a fractional sub-diffusion equation with Dirichlet condition, respectively. We have given the series solution of equation and proved the stability and the convergence of the implicit numerical scheme. It is found that the numerical results are in satisfactory agreement with the analytical solution. Through the robustness analysis, it is also found that the diffusion processes on fractals are more sensitive to the spectral dimension than to the anomalous diffusion exponent.
WOS标题词	Science & Technology ; Physical Sciences
类目[WOS]	Mathematics, Applied ; Mathematics
研究领域[WOS]	Mathematics
关键词[WOS]	ANOMALOUS DIFFUSION ; DIFFERENTIAL-EQUATIONS ; DISORDERED MEDIA ; MELLIN TRANSFORM ; RANDOM-WALKS ; ORDER ; DERIVATIVES
收录类别	SCI
语种	英语
WOS记录号	WOS:000382277200001
内容类型	期刊论文
源URL	[http://ir.wipm.ac.cn/handle/112942/9503]
专题	武汉物理与数学研究所_数学物理与应用研究部
作者单位	1.Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China 2.Huazhong Agr Univ, Dept Phys, Coll Sci, Wuhan 430070, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Wenbiao,Yi, Ming. Sturm-Liouville problem and numerical method of fractional diffusion equation on fractals[J]. ADVANCES IN DIFFERENCE EQUATIONS,2016.
APA	Zhang, Wenbiao,&Yi, Ming.(2016).Sturm-Liouville problem and numerical method of fractional diffusion equation on fractals.ADVANCES IN DIFFERENCE EQUATIONS.
MLA	Zhang, Wenbiao,et al."Sturm-Liouville problem and numerical method of fractional diffusion equation on fractals".ADVANCES IN DIFFERENCE EQUATIONS (2016).