The prototype of spectral methods for the solution of differential problems is the well-known Fourier method which consists of representating the solution as a truncated series expansion, the unknowns being the expansion coefficients. The Fourier basis is appropriate for periodic problems. For nonperiodic problems, the Chebyshev or Legendre polynomial bases are commonly used, but other basis functions could be considered according to the problem under consideration.


Spectral Method Chebyshev Polynomial Domain Decomposition Method Fast Fourier Transform Algorithm Chebyshev Approximation 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Roger Peyret
    • 1
  1. 1.Laboratoire J.A. DieudonnéUniversité de Nice-Sophia AntipolisNiceFrance

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