MATH-452 / 5 crédits

Enseignant: Rosilho De Souza Giacomo

Langue: Anglais

## 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.

## Keywords

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

## 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

## 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

• Semestre: Automne
• Forme de l'examen: Ecrit (session d'hiver)
• Matière examinée: Numerical integration of dynamical systems
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Automne
• Forme de l'examen: Ecrit (session d'hiver)
• Matière examinée: Numerical integration of dynamical systems
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Automne
• Forme de l'examen: Ecrit (session d'hiver)
• Matière examinée: Numerical integration of dynamical systems
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Automne
• Forme de l'examen: Ecrit (session d'hiver)
• Matière examinée: Numerical integration of dynamical systems
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Automne
• Forme de l'examen: Ecrit (session d'hiver)
• Matière examinée: Numerical integration of dynamical systems
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Automne
• Forme de l'examen: Ecrit (session d'hiver)
• Matière examinée: Numerical integration of dynamical systems
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines

## Semaine de référence

 Lu Ma Me Je Ve 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