# Coursebooks

## Numerical integration of dynamical systems

#### Lecturer(s) :

Rosilho De Souza Giacomo

English

#### Summary

In this course we will introduce and study numerical integrators for multi-scale (or stiff) differential equations and dynamical systems with special geometric structures (symplecticity, reversibility, first integrals, etc.). These numerical methods are important for many applications.

#### Content

- Numerical integration of multi-scale or stiff  differential equations.

- Numerical methods preserving geometric structures of dynamical systems (Hamiltonian systems, reversible systems, systems with first integrals, etc.

#### Keywords

stiff differential equations, multiscale problems, Hamiltonian systems, geometric numerical integration

#### Learning Prerequisites

##### Required courses

Advanced Analysis, Linear Algebra, Numerical Analysis

#### Learning Outcomes

By the end of the course, the student must be able to:
• Identify stiff and Hamiltonian differential equations
• Analyze geometric and stability properties of differential equations
• Choose an appropriate method for the solution of stiff or Hamiltonian differential equations
• Analyze geometric and stability properties of numerical methods
• Implement numerical methods for solving stiff or Hamiltonian differential equations

#### Teaching methods

Ex cathedra lecture, exercises in classroom and with computer

#### Expected student activities

Attendance of lectures.

Completing exercises.

Solving problems on the computer.

#### Assessment methods

Written

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

#### Supervision

 Office hours Yes Assistants Yes

#### Resources

##### Bibliography

E. Hairer ans G. Wanner, "Solving Ordinary Differential Equations II", second revised edition, Springer, Berlin, 1996
E. Hairer, C Lubich and G. Wanner, "Geometric Numerical Integration", second edition, Springer, Berlin, 2006

### Reference week

MoTuWeThFr
8-9 MAA110
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17  MAA112
17-18
18-19
19-20
20-21
21-22

Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German