AMATH 571
SLN 10220, MW 3:30-4:50, MGH 228
Spectral Methods
Tentative list of topics to be covered:
- Fourier series approximation of functions and derivatives
- Accuracy of approximation
- The fast Fourier transform (FFT)
- Fourier spectral methods for differential equations
- Polynomial interpolation
- Chebyshev and Legendre polynomials
- (Pseudo) spectral methods based on polynomial approximation
- FFT methods for polynomials
- Stability theory for time dependent problems
Additional topics will depend in part on the interests of the students, and
may include:
- Spectral element methods for complex geometries
- Spectral filtering for discontinous functions (e.g. shock wave problems)
- The chebfun package for manipulating functions in Matlab
- Spectral deferred correction methods for spectral accuracy in time
- Spherical harmonics for geophysical problems
- Quadrature formulas and integral equations
- Eigenvalue problems
- Sinc functions and local Fourier methods