MATH-452 / 5 credits

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

## 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

 Office hours Yes Assistants Yes Forum 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.

## In the programs

• Semester: Spring
• Exam form: Written (summer session)
• 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
• Type: optional
• Semester: Spring
• Exam form: Written (summer session)
• 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
• Type: optional
• Semester: Spring
• Exam form: Written (summer session)
• 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
• Type: optional
• Semester: Spring
• Exam form: Written (summer session)
• 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
• Type: optional
• Semester: Spring
• Exam form: Written (summer session)
• 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
• Type: optional
• Semester: Spring
• Exam form: Written (summer session)
• 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
• Type: optional

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