A superlinear convergence scheme for the multi-term and distribution-order fractional wave equation with initial singularity

doi:10.1002/num.22773

CSpace

	A superlinear convergence scheme for the multi-term and distribution-order fractional wave equation with initial singularity
	Huang, Jianfei 1; Zhang, Jingna 1; Arshad, Sadia 2; Tang, Yifa 3,4
	2021-01-22
发表期刊	NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
ISSN	0749-159X
页码	16
摘要	In this paper, a superlinear convergence scheme for the multi-term and distribution-order fractional wave equation with initial singularity is proposed. The initial singularity of the solution of the multi-term time fractional partial differential equation often generate a singular source, it increases the difficulty to numerically solve the equation. Thus, after discretizing the spatial distribution-order derivative by the midpoint quadrature, an integral transformation is applied to deal with the temporal direction for obtaining a temporal superlinear convergence scheme based on the uniform mesh. Then, the fully discrete scheme is constructed by using Crank-Nicolson technique and L1 approximation in time, and fractional centered difference approximation in space. The convergence and stability of the proposed scheme are rigorously analyzed. Finally, numerical experiments are presented to support the theoretical results of our scheme.
关键词	distribution-order derivative fractional wave equations initial singularity multi-term fractional derivatives superlinear convergence
DOI	10.1002/num.22773
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[11871065]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000609934200001
出版者	WILEY
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58068
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, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Huang, Jianfei,Zhang, Jingna,Arshad, Sadia,et al. A superlinear convergence scheme for the multi-term and distribution-order fractional wave equation with initial singularity[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,2021:16.
APA	Huang, Jianfei,Zhang, Jingna,Arshad, Sadia,&Tang, Yifa.(2021).A superlinear convergence scheme for the multi-term and distribution-order fractional wave equation with initial singularity.NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,16.
MLA	Huang, Jianfei,et al."A superlinear convergence scheme for the multi-term and distribution-order fractional wave equation with initial singularity".NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS (2021):16.