Nonlinear physics
Numerical methods for complex systems II
Summer semester 2017
Lecture with tutorials
Course number in the course overview: 118285
Lecturers, organization, dates & exams
Lecturer
ITP, Wilhelm-Klemm-Straße 9, 48149 Münster, room 316
Tel.: +49 251 83-34923, email: gurevics(at)uni-muenster.deDates & locations
Lecture Thu., 12:20–13:50 KP/TP 304 Start: 20.04.2017 Tutorials Thu., 12:20–13:50 KP/TP 304 Start: on arrangement Credit
The mere attendance of the lecture is valued at 2 CP. If the tutorials are completed as well (> 70 %), 3 CP are awarded. For this, the solutions to the problems must be handed in before the next lecture. If needed, a grade can also be awarded based on the solved problems.
Contents & literature
Contents of the lecture
The lecture treats numerical methods for the solution of partial differential equations which describe structure formation in systems far from stability:
- Transport equations
- Cahn-Hilliard equation
- Real and complex Ginzburg-Landau equations
- Reaction–diffusion equations
- Real and complex Swift-Hohenberg equations
- Rayleigh-Bénard systems
Literature
- Lloyd N. Trefethen, Spectral Methods in MATLAB, illustrated edition. (SIAM: Society for Industrial and Applied Mathematics, 2001)
- Claudio Canuto et al., Spectral Methods in Fluid Dynamics (Springer, 1993)
- John P. Boyd, Chebyshev and Fourier Spectral Methods: Second Revised Edition, 2. ed. (Dover Publications, 2001)
- Michael Bestehorn, Hydrodynamik und Strukturbildung. Mit einer kurzen Einführung in die Kontinuumsmechanik, 1. ed. (Springer, Berlin, 2006)
- William H. Press et al., Numerical Recipes in C: The Art of Scientific Computing, 2. ed. (Cambridge University Press, 1992)
- Scott A. Sarra, Chebyshev Interpolation: An Interactive Tour, Journal of Online Mathematics and Its Applications, Vol.6, ID 1297, (2006)
Lecture material
Lecture notes
- Introduction
- Runge-Kutta Methods
- Pseospectral method
- Burgers Equation
- ETD Methods
- Kdv-Gleichung
- GLE
- References
Further info
Problem sheets
Problems and example programs
Aufgaben
Musterlösung Blatt 1 Fft Training Blatt 2 Rk4 Revisited Blatt 3 Difburgers Blatt 4 Blatt 5 Blatt6