Theory of spectral methods
Abstract
The construction of spectral approximations to time dependent mixed initial boundary value problems is described. The Fourier methods include the Galerkin method and the pseudospectral method. The polynomial methods include a Galerkin method, a pseudospectral Chebyshev method, a pseudospectral Legendre method, and a Tau-Legendre method. A theory of the approximations of the solutions and its derivatives is presented. A stability analysis of pseudospectral schemes is included.
- Publication:
-
In Von Karman Inst. for Fluid Dynamics Computational Fluid Dynamics
- Pub Date:
- 1985
- Bibcode:
- 1985cofd....2Q....G
- Keywords:
-
- Approximation;
- Boundary Value Problems;
- Computational Fluid Dynamics;
- Spectra;
- Time Dependence;
- Chebyshev Approximation;
- Computerized Simulation;
- Fourier Analysis;
- Galerkin Method;
- Legendre Functions;
- Numerical Stability;
- Fluid Mechanics and Heat Transfer