A RBF meshless approach for modeling a fractal mobile/immobile transport model

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	A RBF meshless approach for modeling a fractal mobile/immobile transport model
	Liu, Q. ; Liu, F. ; Turner, I. ; Anh, V. ; Gu, Y. T. ; Liu FW(刘发旺)
刊名	http://dx.doi.org/10.1016/j.amc.2013.10.008
	2014
关键词	ANOMALOUS SUBDIFFUSION EQUATION DIFFUSION EQUATION SOLUTE TRANSPORT MASS-TRANSFER
英文摘要	National Natural Science Foundation of China [11101344, 11001090]; Natural Science Foundation of Fujian [2010J01011, 2013J01021]; ARC [FT100100172]; A fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions,(RBFs) to discretize the space variable. In contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example which is presented to describe a fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating fractional differential equations, and it has good potential in the development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations. Crown copyright (C) 2013 Published by Elsevier Inc. All rights reserved.
语种	英语
出版者	ELSEVIER SCIENCE INC
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/91389]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Liu, Q.,Liu, F.,Turner, I.,et al. A RBF meshless approach for modeling a fractal mobile/immobile transport model[J]. http://dx.doi.org/10.1016/j.amc.2013.10.008,2014.
APA	Liu, Q.,Liu, F.,Turner, I.,Anh, V.,Gu, Y. T.,&刘发旺.(2014).A RBF meshless approach for modeling a fractal mobile/immobile transport model.http://dx.doi.org/10.1016/j.amc.2013.10.008.
MLA	Liu, Q.,et al."A RBF meshless approach for modeling a fractal mobile/immobile transport model".http://dx.doi.org/10.1016/j.amc.2013.10.008 (2014).