ALTERNATING DIRECTION IMPLICIT SCHEMES FOR THE TWO-DIMENSIONAL TIME FRACTIONAL NONLINEAR SUPER-DIFFUSION EQUATIONS

doi:10.4208/jcm.1802-m2017-0196

	ALTERNATING DIRECTION IMPLICIT SCHEMES FOR THE TWO-DIMENSIONAL TIME FRACTIONAL NONLINEAR SUPER-DIFFUSION EQUATIONS
	Huang, Jianfei 1; Zhao, Yue 2,3; Arshad, Sadia 4; Li, Kuangying 5; Tang, Yifa2,3
	2019
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	37 期号:3 页码:297-315
摘要	As is known, there exist numerous alternating direction implicit (ADI) schemes for the two-dimensional linear time fractional partial differential equations (PDEs). However, if the ADI schemes for linear problems combined with local linearization techniques are applied to solve nonlinear problems, the stability and convergence of the methods are often not clear. In this paper, two ADI schemes are developed for solving the two-dimensional time fractional nonlinear super-diffusion equations based on their equivalent partial integro-differential equations. In these two schemes, the standard second-order central difference approximation is used for the spatial discretization, and the classical first-order approximation is applied to discretize the Riemann-Liouville fractional integral in time. The solvability, unconditional stability and L-2 norm convergence of the proposed ADI schemes are proved rigorously. The convergence order of the schemes is O(tau + h(x)(2) + h(y)(2)), where tau is the temporal mesh size, h(x) and h(y) are spatial mesh sizes in the x and y directions, respectively. Finally, numerical experiments are carried out to support the theoretical results and demonstrate the performances of two ADI schemes.
关键词	Time fractional super-diffusion equation Nonlinear system ADI schemes Stability Convergence
DOI	10.4208/jcm.1802-m2017-0196
语种	英语
资助项目	National Natural Science Foundation of China[11701502] ; National Natural Science Foundation of China[11771438]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000455999600001
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32260
专题	计算数学与科学工程计算研究所
通讯作者	Huang, Jianfei
作者单位	1.Yangzhou Univ, Coll Math Sci, Yangzhou 225002, Jiangsu, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.COMSATS Inst Informat Technol, Lahore, Pakistan 5.Univ Tulsa, McDougall Sch Petr Engn, Tulsa, OK 74104 USA
推荐引用方式 GB/T 7714	Huang, Jianfei,Zhao, Yue,Arshad, Sadia,et al. ALTERNATING DIRECTION IMPLICIT SCHEMES FOR THE TWO-DIMENSIONAL TIME FRACTIONAL NONLINEAR SUPER-DIFFUSION EQUATIONS[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2019,37(3):297-315.
APA	Huang, Jianfei,Zhao, Yue,Arshad, Sadia,Li, Kuangying,&Tang, Yifa.(2019).ALTERNATING DIRECTION IMPLICIT SCHEMES FOR THE TWO-DIMENSIONAL TIME FRACTIONAL NONLINEAR SUPER-DIFFUSION EQUATIONS.JOURNAL OF COMPUTATIONAL MATHEMATICS,37(3),297-315.
MLA	Huang, Jianfei,et al."ALTERNATING DIRECTION IMPLICIT SCHEMES FOR THE TWO-DIMENSIONAL TIME FRACTIONAL NONLINEAR SUPER-DIFFUSION EQUATIONS".JOURNAL OF COMPUTATIONAL MATHEMATICS 37.3(2019):297-315.