# Fiches de cours

## Numerical integration of dynamical systems

English

#### Remarque

pas donné en 2019-20

#### 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.

#### Learning Prerequisites

##### Recommended courses

Analysis, 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

#### 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

### Dans les plans d'études

• Mathématiques, 2019-2020, Bachelor semestre 6
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
5
• Matière examinée
Numerical integration of dynamical systems
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
2 Heure(s) hebdo x 14 semaines
• Science et ingénierie computationnelles, 2019-2020, Master semestre 2
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
5
• Matière examinée
Numerical integration of dynamical systems
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
2 Heure(s) hebdo x 14 semaines
• Science et ingénierie computationnelles, 2019-2020, Master semestre 4
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
5
• Matière examinée
Numerical integration of dynamical systems
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
2 Heure(s) hebdo x 14 semaines

LuMaMeJeVe
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
En construction
Cours
Exercice, TP
Projet, autre

### légende

• Semestre d'automne
• Session d'hiver
• Semestre de printemps
• Session d'été
• Cours en français
• Cours en anglais
• Cours en allemand