RATIONAL SPECTRAL METHODS FOR PDEs INVOLVING FRACTIONAL LAPLACIAN IN UNBOUNDED DOMAINS

doi:10.1137/19M1244299

CSpace

	RATIONAL SPECTRAL METHODS FOR PDEs INVOLVING FRACTIONAL LAPLACIAN IN UNBOUNDED DOMAINS
	Tang, Tao 1,2; Wang, Li-Lian 3; Yuan, Huifang 4; Zhou, Tao 5,6
	2020
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	42 期号:2 页码:A585-A611
摘要	Many PDEs involving fractional Laplacian are naturally set in unbounded domains with underlying solutions decaying slowly and subject to certain power law. Their numerical solutions are underexplored. This paper aims at developing accurate spectral methods using rational basis (or modified mapped Gegenbauer functions) for such models in unbounded domains. The main building block of the spectral algorithms is the explicit representations for the Fourier transform and fractional Laplacian of the rational basis, derived from some useful integral identities related to modified Bessel functions. With these at our disposal, we can construct rational spectral-Galerkin and direct collocation schemes by precomputing the associated fractional differentiation matrices. We obtain optimal error estimates of rational spectral approximation in the fractional Sobolev spaces and analyze the optimal convergence of the proposed Galerkin scheme. We also provide ample numerical results to show that the rational method outperforms the Hermite function approach.
关键词	fractional Laplacian Gegenbauer polynomials modified rational functions unbounded domains Fourier transforms spectral methods
DOI	10.1137/19M1244299
收录类别	SCI
语种	英语
资助项目	NSF of China[11822111] ; NSF of China[11688101] ; NSF of China[11571351] ; NSF of China[11731006] ; Science Challenge Project[TZ2018001] ; Singapore MOE AcRF Tier 2 grants[MOE2018-T2-1-059] ; Singapore MOE AcRF Tier 2 grants[MOE2017-T2-2-144] ; Hong Kong Ph.D. fellowship ; Youth Innovation Promotion Association (CAS)
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000551251700015
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51883
专题	中国科学院数学与系统科学研究院
通讯作者	Tang, Tao
作者单位	1.BNUH KBU United Int Coll, Div Sci & Technol, Zhuhai, Guangdong, Peoples R China 2.Southern Univ Sci & Technol, SUSTech Int Ctr Math, Shenzhen, Peoples R China 3.Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore 4.Hong Kong Baptist Univ, Dept Math, Hong Kong, Peoples R China 5.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing, Peoples R China 6.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Tang, Tao,Wang, Li-Lian,Yuan, Huifang,et al. RATIONAL SPECTRAL METHODS FOR PDEs INVOLVING FRACTIONAL LAPLACIAN IN UNBOUNDED DOMAINS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2020,42(2):A585-A611.
APA	Tang, Tao,Wang, Li-Lian,Yuan, Huifang,&Zhou, Tao.(2020).RATIONAL SPECTRAL METHODS FOR PDEs INVOLVING FRACTIONAL LAPLACIAN IN UNBOUNDED DOMAINS.SIAM JOURNAL ON SCIENTIFIC COMPUTING,42(2),A585-A611.
MLA	Tang, Tao,et al."RATIONAL SPECTRAL METHODS FOR PDEs INVOLVING FRACTIONAL LAPLACIAN IN UNBOUNDED DOMAINS".SIAM JOURNAL ON SCIENTIFIC COMPUTING 42.2(2020):A585-A611.