Hyperbolic systems of partial differential equations (PDE) play an important role in many applications, such as fluid dynamics, wave propagation and electromagnetics. The purpose of the course is to introduce the basic theory for such systems, and the construction and analysis of difference methods for their numerical solution. In the first part of the course, the basic concepts such as wellposedness and stability will be introduced. The methods for analysis are based on Fourier analysis for the pure initial value problems, and on the energy method and the Laplace transform method for the initial-boundary value problems. The connection and similarities between the analysis technique for the continuous and discrete case will be demonstrated. In the computer laboratory exercises, simple model problems will be solved numerically in order to illustrate the theory.
A priori knowledge of difference methods for ordinary differential equations is helpful.
The course is based on the new book:
H.-O. Kreiss and H.U. Busenhart: Time-dependent Partial Differential Equations and Their Numerical Solution. Lectures in Mathematics, ETH Zurich, Birkhauser (2001), 82 pages. ISBN 3-7643-6125-5.