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.
KeywordsSpectral Method Chebyshev Polynomial Domain Decomposition Method Fast Fourier Transform Algorithm Chebyshev Approximation
Unable to display preview. Download preview PDF.