Convolution Quadrature Methods for Time-Space Fractional Nonlinear Diffusion-Wave Equations

doi:10.4208/eajam.230718.131018

	Convolution Quadrature Methods for Time-Space Fractional Nonlinear Diffusion-Wave Equations
	Huang, Jianfei 1; Arshad, Sadia 2; Jiao, Yandong 3; Tang, Yifa4,5
	2019-08-01
发表期刊	EAST ASIAN JOURNAL ON APPLIED MATHEMATICS
ISSN	2079-7362
卷号	9 期号:3 页码:538-557
摘要	Two second-order convolution quadrature methods for fractional nonlinear diffusion-wave equations with Caputo derivative in time and Riesz derivative in space are constructed. To improve the numerical stability, the fractional diffusion-wave equations are firstly transformed into equivalent partial integro-differential equations. Then, a second-order convolution quadrature is applied to approximate the Riemann-Liouville integral. This deduced convolution quadrature method can handle solutions with low regularity in time. In addition, another second-order convolution quadrature method based on a new second-order approximation for discretising the Riemann-Liouville integral at time t(k-1/2) is constructed. This method reduces computational complexity if Crank-Nicolson technique is used. The stability and convergence of the methods are rigorously proved. Numerical experiments support the theoretical results.
关键词	Fractional diffusion-wave equation nonlinear source convolution quadrature generating function stability and convergence
DOI	10.4208/eajam.230718.131018
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
WOS记录号	WOS:000470088100008
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/34852
专题	计算数学与科学工程计算研究所
通讯作者	Jiao, Yandong
作者单位	1.Yangzhou Univ, Coll Math Sci, Yangzhou 225002, Jiangsu, Peoples R China 2.COMSATS Inst Informat Technol, Lahore, Pakistan 3.Hebei Univ Technol, Sch Sci, Tianjin 300401, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 5.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Huang, Jianfei,Arshad, Sadia,Jiao, Yandong,et al. Convolution Quadrature Methods for Time-Space Fractional Nonlinear Diffusion-Wave Equations[J]. EAST ASIAN JOURNAL ON APPLIED MATHEMATICS,2019,9(3):538-557.
APA	Huang, Jianfei,Arshad, Sadia,Jiao, Yandong,&Tang, Yifa.(2019).Convolution Quadrature Methods for Time-Space Fractional Nonlinear Diffusion-Wave Equations.EAST ASIAN JOURNAL ON APPLIED MATHEMATICS,9(3),538-557.
MLA	Huang, Jianfei,et al."Convolution Quadrature Methods for Time-Space Fractional Nonlinear Diffusion-Wave Equations".EAST ASIAN JOURNAL ON APPLIED MATHEMATICS 9.3(2019):538-557.