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On spectral approximations in elliptical geometries using Mathieu functions


Authors: Jie Shen and Li-Lian Wang
Journal: Math. Comp. 78 (2009), 815-844
MSC (2000): Primary 65N35, 65N22, 65F05, 35J05
DOI: https://doi.org/10.1090/S0025-5718-08-02197-2
Published electronically: November 20, 2008
MathSciNet review: 2476561
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider in this paper approximation properties and applications of Mathieu functions. A first set of optimal error estimates are derived for the approximation of periodic functions by using angular Mathieu functions. These approximation results are applied to study the Mathieu-Legendre approximation to the modified Helmholtz equation and Helmholtz equation. Illustrative numerical results consistent with the theoretical analysis are also presented.


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Additional Information

Jie Shen
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: shen@math.purdue.edu

Li-Lian Wang
Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637616, Singapore
Email: lilian@ntu.edu.sg

DOI: https://doi.org/10.1090/S0025-5718-08-02197-2
Keywords: Mathieu functions, elliptic coordinates, approximation in Sobolev spaces, Helmholtz equations
Received by editor(s): March 4, 2008
Published electronically: November 20, 2008
Additional Notes: The work of the first author was partially supported by NSF Grant DMS-0610646.
The work of the second author was partially supported by a Start-Up grant from NTU, Singapore MOE Grant T207B2202, and Singapore NRF2007IDM-IDM002-010.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.