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RATIONAL SPECTRAL METHODS FOR PDEs INVOLVING FRACTIONAL LAPLACIAN IN UNBOUNDED DOMAINS

文献类型：期刊论文

作者Tang, Tao5,6; Wang, Li-Lian1; Yuan, Huifang2; Zhou, Tao3,4
刊名SIAM JOURNAL ON SCIENTIFIC COMPUTING
出版日期2020
卷号42期号:2页码:A585-A611
关键词fractional Laplacian Gegenbauer polynomials modified rational functions unbounded domains Fourier transforms spectral methods
ISSN号1064-8275
DOI10.1137/19M1244299
英文摘要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.
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
语种英语
WOS记录号WOS:000551251700015
出版者SIAM PUBLICATIONS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/51882]  
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.Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore
2.Hong Kong Baptist Univ, Dept Math, Hong Kong, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing, Peoples R China
4.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS, Beijing, Peoples R China
5.BNUH KBU United Int Coll, Div Sci & Technol, Zhuhai, Guangdong, Peoples R China
6.Southern Univ Sci & Technol, SUSTech Int Ctr Math, Shenzhen, 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.

入库方式： OAI收割

来源：数学与系统科学研究院

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