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Fiches de cours
Numerical integration of dynamical systems
MATH-452
Enseignant(s) :
Rosilho De Souza GiacomoLangue:
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
Ressources en bibliothèque
Dans les plans d'études
- SemestreAutomne
- Forme de l'examenEcrit
- 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
- Semestre
- SemestreAutomne
- Forme de l'examenEcrit
- 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
- Semestre
- SemestreAutomne
- Forme de l'examenEcrit
- 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
- Semestre
- SemestreAutomne
- Forme de l'examenEcrit
- 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
- Semestre
- SemestreAutomne
- Forme de l'examenEcrit
- 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
- Semestre
- SemestreAutomne
- Forme de l'examenEcrit
- 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
- Semestre
Semaine de référence
Lu | Ma | Me | Je | Ve | |
---|---|---|---|---|---|
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 |
légende
- Semestre d'automne
- Session d'hiver
- Semestre de printemps
- Session d'été
- Cours en français
- Cours en anglais
- Cours en allemand