Some Recent Advances on Spectral Methods for Unbounded Domains
Jie Shen 1*, Li-Lian Wang 21 Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA.
2 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637616, Singapore.
Received 13 January 2008; Accepted (in revised version) 8 June 2008
Available online 1 August 2008
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.AMS subject classifications: 65N35, 65N22,65F05, 35J05
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Key words: Spectral method, unbounded domain, orthogonal polynomials, rational functions, Hermite functions, Laguerre functions.
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