A numerical method for two-dimensional multi-term time-space fractional nonlinear diffusion-wave equations

doi:10.1016/j.apnum.2020.09.003

CSpace

	A numerical method for two-dimensional multi-term time-space fractional nonlinear diffusion-wave equations
	Huang, Jianfei 1; Zhang, Jingna 1; Arshad, Sadia 2; Tang, Yifa 3,4
	2021
发表期刊	APPLIED NUMERICAL MATHEMATICS
ISSN	0168-9274
卷号	159 页码:159-173
摘要	Recently, 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.
关键词	Multi-term time-space derivatives Fractional nonlinear diffusion-wave equations Finite difference schemes Stability Convergence Fast ADI scheme
DOI	10.1016/j.apnum.2020.09.003
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11701502] ; National Natural Science Foundation of China[11426141] ; National Natural Science Foundation of China[11871065]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000581768900010
出版者	ELSEVIER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52407
专题	中国科学院数学与系统科学研究院
通讯作者	Huang, Jianfei
作者单位	1.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
推荐引用方式 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.