An Introduction to Spectral Methods
Preliminaries
1. Floating-point numbers
Spectral Methods
1. Spectral methods
2. Method of weighted residuals
3. Fourier series
4. Chebyshev polynomials
5. Linear stationary case
6. Nonlinear problems
7. Pseudo-spectral method and aliasing errors
8. NB Numerical accuracy
9. NB. Interpolation and Integration
10. NB. Fourier wavenumbers
11. NB. Fourier Transform
12. NB. Chebyshev Polynomials
13. NB. Linear Stability Analysis Using Orr-Sommerfeld Equation
14. NB. Burgers equation
Index
