Spectral collocation methods
This is a survey article on the application of spectral collocation methods to the solution of partial differential equations. For the most part, the basis functions used are either trigonometric or Chebyshev polynomials, although there is some discussion of Legendre polynomials. In the first half of the article theoretical results on stability and accuracy are presented. No proofs are given, but there is adequate reference to the literature. The second half of the article is devoted to a discussion of considerations to be faced in the application of the methods to practical problems. Here the authors take up such questions as iterative methods and preconditioners for implicit versions of the method, smoothing methods to remove spurious oscillations near sharp gradients, and domain decomposition methods for complex geometries.
scientific article; zbMATH DE number 4098679
scientific article