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Numerical Analysis
Numerische Mathematik
Last Updated: 2026-02-05 15:18:44
Abstract
The central topic is the numerical treatment of ordinary differential equations:One- and multistep methods, explicit, implicit and symplectic methods as well as methods for stochastic differential equations.Iterative methods for large sparse linear systems of equations are covered as well.
Objective
The students should learn the ideas on which the numerical methods are based on. Not only the motivation and derivation of algorithms matters, but also their analysis, like proofs of convergence.
Content
The central topic is the numerical treatment of ordinary differential equations: One- and multistep methods, implicit methods for stiff problems and symplectic methods for problems with intrinsic constraints. Methods for stochastic differential equations. Construction, stability, convergence and efficiency of the methods shall be discussed: Explicit- and implicit methods, one- and multistep methods, symplectic methods and methods for stochastic differential equations. Stability and convergence. Iterative methods for large sparse linear systems of equations are covered as well: Iterative methods for sparse systems (Jacobi, SOR) and the method of conjugate gradients.
Resources
Literature
Deuflhard and Bornemann: Numerische Mathematik II - Integration gewöhnlicher Differentialgleichungen, Walter de Gruyter & Co., 1994. Hairer and Wanner: Solving ordinary differential equations II - Stiff and differential-algebraic problems, Springer-Verlag, 1996. Hairer, Lubich and Wanner: Geometric numerical integration - Structure-preserving algorithms for ordinary differential equations}, Springer-Verlag, Berlin, 2002. Hairer, Norsett and Wanner: Solving ordinary differential equations I - Nonstiff problems, Springer-Verlag, Berlin, 1993. Henrici: Discrete variable method in ordinary differential equations, Wiley, New York, 1962. Kloeden and Platen: Numerical solution of stochastic differential equations, Springer-Verlag, Berlin, 1992. Kloeden, Platen and Schurz: Numerical Solution of SDE Through Computer Experiments, Springer-Verlag, Berlin, 2002. Milstein: Numerical integration of stochastic differential equations, Kluwer Academic Publishers, Dordrecht, 1995. Roman: A short introduction to numerical analysis of stochastic differential equations, IMPA, Rio de Janeiro, 2005. Sauer: Numerical Analysis, Pearson Education, Boston, 2006. Stoer and Bulirsch: Einführung in die Numerische Mathematik II, Springer-Verlag, Berlin, 1973. Walter: Gewöhnliche Differentialgleichungen - Eine Einführung, Springer-Verlag, Berlin, 1972. Walter: Ordinary differential equations, Springer-Verlag, New York, 1998.
General Information
- Language
- German
- Levels
- BSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- written 150 minutes
- Aids
- Prüfung am Computer (von der ETH gestellt); keine anderen Hilfsmittel
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Numerische Mathematik |
|
3 h weekly |
| exercise | Numerische Mathematik |
|
2 h weekly |