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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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On spectral approximations in elliptical geometries using Mathieu functions
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by Jie Shen and Li-Lian Wang PDF
Math. Comp. 78 (2009), 815-844 Request permission

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
  • MR Author ID: 257933
  • ORCID: 0000-0002-4885-5732
  • Email: shen@math.purdue.edu
  • Li-Lian Wang
  • Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637616, Singapore
  • MR Author ID: 681795
  • Email: lilian@ntu.edu.sg
  • 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.
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2476561