Nonlinear physics
Numerical methods for complex systems II
Summer semester 2016
Lecture with tutorials
Course number in the course overview: 114329
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: 14.04.2016 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
- Pseodospectral method for nonlinear PDEs
- Burgers Equation
- Korteweg-de Vries Equation
- Cahn-Hilliard Equation
- Swift-Hohenberg Equation
- Ginzburg-Landau Equation
- Reaction-Diffusion Systems
- Runge-Kutta Methods
- Ordering of Fourier Coefficients
- ETD and IF Methods
- References
Further info
Tutorials
Coordination: Markus Wilczek
Solutions must be handed in via email to
- Markus Wilczek, markuswilczek(at)uni-muenster.de
- Subject: [Numerik-Abgabe] Blatt x - Name
The hand-ins should consists of the used program code and a PDF document which also shows images of the simulation results. Questions about the tutorials can also be sent to this address; please use the subject „[Numerik-Frage] …“
The designated programming language for this lecture is Python. Questions about implementations in other languages can only be answered in a limited way.
Problem sheets
Problems and example programs