The case study for the Fourier method will employ the nonlinear Schrödinger/Ginzburg-Landau equation, which describes, for instance, phase transitions, soliton pulses in fiber optics, weakly nonlinear waves in general,... In the Chebyshev project a set of equations will be solved which describe oscillatory and pattern-forming chemical reactions. In both projects graphical animation will aid the developing of the codes as well as the interpretation of the results. In particular the Fourier-spectral code will enable the students to solve efficiently a large variety of other partial differential equations without too much modification.
The technical topics to be discussed will include:
Approximation properties of Fourier and Chebyshev series, pseudo-spectral vs. Galerkin methods, review of time-stepping methods (stability), initial-boundary-value problems, Chebyshev-tau method, iterative methods (implicit schemes, preconditioning), higher-dimensional problems.
Strongly recommended book:
C. Canuto et al., Spectral Methods in Fluid Dynamics, Springer.
Time and Place: Tu Th 2:30-4:00 in A110 (computer projection room)
Do you have any questions?
Phone: 491-8316, e-mail: firstname.lastname@example.org