Fiches de cours

Numerical integration of dynamical systems

MATH-452

Enseignant(s) :

Rosilho De Souza Giacomo

Langue:

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

• Geometric Numerical Integration / Hairer
• Solving Ordinary Differential Equations II / Hairer