Some Recent Advances on SpectralMethods for Unbounded Domains

作     者：Jie Shen Li-Lian Wang 

作者机构：Department of MathematicsPurdue UniversityWest LafayetteIN47907USA Division of Mathematical SciencesSchool of Physical and Mathematical SciencesNanyang Technological University637616Singapore 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2009年第5卷第2期

页      面：195-241页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0702[理学-物理学] 070101[理学-基础数学] 

基　　金：The work of J.S.is partially supported by the NFS grant DMS-0610646 The work of L.W.is partially supported by a Start-Up grant from NTU and by Singapore MOE Grant T207B2202 Singapore grant NRF 2007IDM-IDM002-010 

主　　题：Spectral method unbounded domain orthogonal polynomials rational functions Hermite functions Laguerre functions 

摘      要：We present in this paper a unified framework for analyzing the spectral methods in unbounded domains using mapped Jacobi,Laguerre and Hermite functions.A detailed comparison of the convergence rates of these spectral methods for solutions with typical decay behaviors is carried out,both theoretically and computationally.A brief review on some of the recent advances in the spectral methods for unbounded domains is also presented.