While spectral methods are generally based on Fourier series or Chebyshev polynomials, non-classical polynomials and associated quadratures are used for many of the applications presented in Spectral Methods in Chemistry and Physics. Fourier series methods are summarized with a discussion of the resolution of the Gibbs phenomenon. Classical and non-classical quadratures are used for the evaluation of integrals in reaction dynamics including nuclear fusion, radial integrals in density functional theory, elastic scattering theory, and other applications. The subject matter includes the calculation of transport coefficients in gases and other gas dynamical problems based on spectral and pseudospectral solutions of the Boltzmann equation. Radiative transfer in astrophysics and atmospheric science, and applications related to space physics are discussed. The relaxation of initial non-equilibrium distributions to equilibrium for several different systems is studied with the Boltzmann and Fokker-Planck equations.
MATLAB codes are provided for most of the numerical results reported in the book.