Hermite Spectral Collocation Methods for Fractional PDEs in Unbounded Domains

doi:10.4208/cicp.2018.hh80.12

	Hermite Spectral Collocation Methods for Fractional PDEs in Unbounded Domains
	Tang, Tao 1; Yuan, Huifang 2; Zhou, Tao3
	2018-10-01
发表期刊	COMMUNICATIONS IN COMPUTATIONAL PHYSICS
ISSN	1815-2406
卷号	24 期号:4 页码:1143-1168
摘要	This work is concerned with spectral collocation methods for fractional PDEs in unbounded domains. The method consists of expanding the solution with proper global basis functions and imposing collocation conditions on the Gauss-Hermite points. In this work, two Hermite-type functions are employed to serve as basis functions. Our main task is to find corresponding differentiation matrices which are computed recursively. Two important issues relevant to condition numbers and scaling factors will be discussed. Applications of the spectral collocation methods to multi-term fractional PDEs are also presented. Several numerical examples are carried out to demonstrate the effectiveness of the proposed methods.
关键词	Fractional PDEs Hermite polynomials/functions unbounded domain spectral collocation methods
DOI	10.4208/cicp.2018.hh80.12
语种	英语
资助项目	Special Project on High-Performance Computing under the National Key RD Program[2016YFB0200604] ; National Natural Science Foundations of China[91630312] ; National Natural Science Foundations of China[91630203] ; National Natural Science Foundations of China[11571351] ; National Natural Science Foundations of China[11731006] ; National Natural Science Foundations of China[11688101] ; Hong Kong PhD Fellowship ; Science Challenge Project[TZ2018001] ; NCMIS ; Youth Innovation Promotion Association of CAS
WOS研究方向	Physics
WOS类目	Physics, Mathematical
WOS记录号	WOS:000455957800010
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/32314
专题	计算数学与科学工程计算研究所
通讯作者	Tang, Tao
作者单位	1.Southern Univ Sci & Technol, Dept Math, Shenzhen, Peoples R China 2.Hong Kong Baptist Univ, Dept Math, Hong Kong, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Tang, Tao,Yuan, Huifang,Zhou, Tao. Hermite Spectral Collocation Methods for Fractional PDEs in Unbounded Domains[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS,2018,24(4):1143-1168.
APA	Tang, Tao,Yuan, Huifang,&Zhou, Tao.(2018).Hermite Spectral Collocation Methods for Fractional PDEs in Unbounded Domains.COMMUNICATIONS IN COMPUTATIONAL PHYSICS,24(4),1143-1168.
MLA	Tang, Tao,et al."Hermite Spectral Collocation Methods for Fractional PDEs in Unbounded Domains".COMMUNICATIONS IN COMPUTATIONAL PHYSICS 24.4(2018):1143-1168.