Numerical methods for partial differential equations
apl. Prof. Dr. Andreas M. Hinz
University of Munich, summer semester 2002
Contents
Partial differential equations play a key role in mathematical modelling of processes in science, technology and finance. Numerical methods to obtain practical solutions are therefore the core of what is now called scientific computing. They are based on discretization and depend on efficient algorithms for solving large algebraic systems. We will present two approaches, the finite difference method and the finite element method, as performed on the model problem of the Poisson equation.
Chapter 0. Introduction
1. Mathematical modelling
2. Analytic properties of partial differential equations
3. Discretization
Chapter 1. Finite Difference Method
4. Time-dependent problems
5. Finite Differences for the Poisson equation
6. Non-linear problems
Chapter 2. Finite Element Method
7. Approximation of solutions
8. Basic ideas of the Finite Element method
9. The Finite Element method for the Poisson equation
Prerequisites
Analysis, linear algebra. Some basic knowledge in numerical analysis and the analytic theory of partial differential equations is useful.
Literature
For the background in real analysis, numerical analysis and partial differential equations:
E. DiBenedetto, Real Analysis, Birkhäuser, Boston, 2002.
W. Gautschi, Numerical Analysis, Birkhäuser, Boston, 1997.
E. DiBenedetto, Partial Differential Equations, Birkhäuser, Boston, 1995.A printed manuscript is available for the students of the course including an annotated list of references.
A. M. Hinz, andreas.hinz@mathematik.uni-muenchen.de, 2002-11-21