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Numerische Mathematik

, Volume 115, Issue 4, pp 511–552 | Cite as

Multivariate modified Fourier series and application to boundary value problems

  • Ben Adcock
Article

Abstract

In this paper we analyse the approximation-theoretic properties of modified Fourier series in Cartesian product domains with coefficients from both full and hyperbolic cross index sets. We show that the number of expansion coefficients may be reduced significantly whilst retaining comparable error estimates. In doing so we extend the univariate results of Iserles, Nørsett and S. Olver. We then demonstrate that these series can be used in the spectral-Galerkin approximation of second order Neumann boundary value problems, which offers some advantages over standard Chebyshev or Legendre polynomial discretizations.

Mathematics Subject Classification (2000)

65T40 65N35 42C15 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.DAMTP, Centre for Mathematical SciencesUniversity of CambridgeCambridgeUK

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