SPECTRAL APPROXIMATIONS

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• The Periodic Problem -- The Fourier Expansion
  • Spectral accuracy
• The Periodic Problem -- The Fourier Interpolant
  • Aliasing and spectral accuracy
  • Fourier differentiation matrix
  • Fourier interpolant revisited on an even number of gridpoints
• The (Pseudo)Spectral Fourier Expansions - Exponential Accuracy
• The Non-Periodic Problem -- The Chebyshev Expansion
  • Spectral accuracy
• The Non-Periodic Problem -- The Chebyshev Interpolant
  • Chebyshev interpolant at Gauss gridpoints
  • Chebyshev interpolant at Gauss-Lobatto gridpoints
  • Exponential convergence of Chebyshev expansions
  • Chebyshev differentiation matrix