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A numerical method for two-dimensional multi-term time-space fractional nonlinear diffusion-wave equations
Huang, Jianfei1; Zhang, Jingna1; Arshad, Sadia2; Tang, Yifa3,4
2021
Source PublicationAPPLIED NUMERICAL MATHEMATICS
ISSN0168-9274
Volume159Pages:159-173
AbstractRecently, numerous numerical schemes have been developed for solving single-term time-space fractional diffusion-wave equations. Among them, some popular methods were constructed by using the graded meshes due to the solution with low temporal regularity. In this paper, we present an efficient alternating direction implicit (ADI) scheme for two-dimensional multi-term time-space fractional nonlinear diffusion-wave equations. Firstly, the considered problem is equivalently transformed into its partial integro-differential form with the Riemann-Liouville integral and multi-term Caputo derivatives. Secondly, the ADI scheme is constructed by using the first-order approximations and L1 approximations to approximate the terms in time, and using the fractional centered differences to discretize the multi-term Riesz fractional derivatives in space. Furthermore, the fast implement of the proposed ADI scheme is discussed by the sum-of-exponentials technique for both Caputo derivatives and Riemann-Liouville integrals. Then, the solvability, unconditional stability and convergence of the proposed ADI scheme are strictly established. Finally, two numerical examples are given to support our theoretical results, and demonstrate the computational performances of the fast ADI scheme. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.
KeywordMulti-term time-space derivatives Fractional nonlinear diffusion-wave equations Finite difference schemes Stability Convergence Fast ADI scheme
DOI10.1016/j.apnum.2020.09.003
Indexed BySCI
Language英语
Funding ProjectNational Natural Science Foundation of China[11701502] ; National Natural Science Foundation of China[11426141] ; National Natural Science Foundation of China[11871065]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000581768900010
PublisherELSEVIER
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/52407
Collection中国科学院数学与系统科学研究院
Corresponding AuthorHuang, Jianfei
Affiliation1.Yangzhou Univ, Coll Math Sci, Yangzhou 225002, Jiangsu, Peoples R China
2.COMSATS Univ Islamabad, Lahore Campus, Lahore, Pakistan
3.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China
4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Huang, Jianfei,Zhang, Jingna,Arshad, Sadia,et al. A numerical method for two-dimensional multi-term time-space fractional nonlinear diffusion-wave equations[J]. APPLIED NUMERICAL MATHEMATICS,2021,159:159-173.
APA Huang, Jianfei,Zhang, Jingna,Arshad, Sadia,&Tang, Yifa.(2021).A numerical method for two-dimensional multi-term time-space fractional nonlinear diffusion-wave equations.APPLIED NUMERICAL MATHEMATICS,159,159-173.
MLA Huang, Jianfei,et al."A numerical method for two-dimensional multi-term time-space fractional nonlinear diffusion-wave equations".APPLIED NUMERICAL MATHEMATICS 159(2021):159-173.
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