Hybrid prolate pseudospectral methods on Chebyshev and Legendre grids I - A preview

Narayan Kovvali*, Wenbin Lin, Lawrence Carin

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The use of prolate spheroidal wave functions as basis functions in the pseudospectral method has been shown to possess strong advantages over the orthogonal polynomials and related functions of conventional pseudospectral methods. The most notable of these is higher accuracy and a smaller number of unknowns for problems involving bandlimited functions. However, when the bandwidth parameter c and unknown number N are large, significant pre-processing effort is involved in computing the prolate collocation grid positions. In this paper, we introduce hybrid prolate-Chebyshev and prolate-Legendre pseudospectral schemes which are based on prolate spheroidal wave functions but employ classic Chebyshev and Legendre Gauss-Lobatto grids for collocation. The hybrid schemes afford less pre-computation overhead compared to pure prolate pseudospectral methods, yielding solutions of higher accuracy than conventional Chebyshev or Legendre pseudospectral methods. The utility of the hybrid algorithms is demonstrated through several numerical examples.

Original languageEnglish
Title of host publicationDISCRETE AND COMPUTATIONAL MATHEMATICS
EditorsF Liu, GM NGuerekata, D Pokrajac, Shi, J Sun, Xia
PublisherNova Science Publishers, Inc.
Pages121-137
Number of pages17
ISBN (Print)978-1-60021-810-1
StatePublished - 2008
Externally publishedYes
EventSummer Workshop on Applied Mathematics - Dover, Germany
Duration: Jul 31 2006Aug 2 2006

Conference

ConferenceSummer Workshop on Applied Mathematics
CountryGermany
CityDover
Period07/31/0608/2/06

Keywords

  • pseudospectral method
  • prolate spheroidal wave functions
  • Chebyshev polynomials
  • Legendre polynomials
  • SPHEROIDAL WAVE-FUNCTIONS
  • FOURIER-ANALYSIS
  • SPECTRAL ELEMENT
  • UNCERTAINTY
  • INTERPOLATION
  • QUADRATURE
  • POINTS

Cite this