Numerical integration of dynamical systems

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

Keywords

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

Learning Prerequisites

Recommended courses

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

Transversal skills

• Use a work methodology appropriate to the task.
• Assess one's own level of skill acquisition, and plan their on-going learning goals.
• Demonstrate the capacity for critical thinking

Teaching methods

Ex cathedra lecture, exercises in classroom and with computer.

Expected student activities

Attendance of the lectures.

Completing the exercises.

Assessment methods

Written examination.

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

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.

Moodle Link

• https://go.epfl.ch/MATH-452