Coursebooks

Numerical integration of dynamical systems

MATH-452

Lecturer(s) :

Rosilho De Souza Giacomo

Language:

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:

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

In the programs

  • Mathematics - master program, 2020-2021, Master semester 1
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Numerical integration of dynamical systems
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics - master program, 2020-2021, Master semester 3
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Numerical integration of dynamical systems
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Applied Mathematics, 2020-2021, Master semester 1
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Numerical integration of dynamical systems
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Applied Mathematics, 2020-2021, Master semester 3
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Numerical integration of dynamical systems
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Computational science and Engineering, 2020-2021, Master semester 1
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Numerical integration of dynamical systems
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Computational science and Engineering, 2020-2021, Master semester 3
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Numerical integration of dynamical systems
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks

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

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