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Numerical Analysis
Numerische Mathematik
Last Updated: 2026-02-05 15:29:11
Abstract
The central topic of this course is the numerical treatment of ordinary differential equations. This includes Runge-Kutta methods, multistep methods, and structure preserving numerical integration, as well as methods for stochastic differential equations.The course covers the derivation of the methods, their implementation, and theoretical analysis.
Objective
The course aims to impart knowledge about important numerical methods for the solution of ordinary and stochastic differential equations. This includes familiarity with their main ideas, awareness of their advantages and limitations, and techniques for investigating stability and convergence. Further, students should know about structural properties of ordinary diferential equations and how to use them as guideline for the selection of numerical integration schemes. They should also acquire the skills to implement numerical integrators in MATLAB and test them in numerical experiments.
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.
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 |