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Analysis of spectral approximations using prolate spheroidal wave functions


Author: Li-Lian Wang
Journal: Math. Comp. 79 (2010), 807-827
MSC (2000): Primary 65N35, 65N22, 65F05, 35J05
DOI: https://doi.org/10.1090/S0025-5718-09-02268-6
Published electronically: September 17, 2009
MathSciNet review: 2600544
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Abstract: In this paper, the approximation properties of the prolate spheroidal wave functions of order zero (PSWFs) are studied, and a set of optimal error estimates are derived for the PSWF approximation of non-periodic functions in Sobolev spaces. These results serve as an indispensable tool for the analysis of PSWF spectral methods. A PSWF spectral-Galerkin method is proposed and analyzed for elliptic-type equations. Illustrative numerical results consistent with the theoretical analysis are also presented.


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Additional Information

Li-Lian Wang
Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
Email: lilian@ntu.edu.sg

DOI: https://doi.org/10.1090/S0025-5718-09-02268-6
Keywords: Prolate spheroidal wave functions, bandlimited functions, approximations in Sobolev spaces, spectral methods, quasi-uniform grids
Received by editor(s): July 16, 2008
Received by editor(s) in revised form: December 30, 2008
Published electronically: September 17, 2009
Additional Notes: This work is partially supported by AcRF Tier 1 Grant RG58/08, Singapore MOE Grant T207B2202, and Singapore NRF2007IDM-IDM002-010.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.