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ALTERNATING DIRECTION IMPLICIT SCHEMES FOR THE TWO-DIMENSIONAL TIME FRACTIONAL NONLINEAR SUPER-DIFFUSION EQUATIONS
Huang, Jianfei1; Zhao, Yue2,3; Arshad, Sadia4; Li, Kuangying5; Tang, Yifa2,3
2019
Source PublicationJOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN0254-9409
Volume37Issue:3Pages:297-315
AbstractAs 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.
KeywordTime fractional super-diffusion equation Nonlinear system ADI schemes Stability Convergence
DOI10.4208/jcm.1802-m2017-0196
Language英语
Funding ProjectNational Natural Science Foundation of China[11701502] ; National Natural Science Foundation of China[11771438]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000455999600001
PublisherGLOBAL SCIENCE PRESS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/32260
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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