Advanced numerical analysis II
Summary
The student will learn state-of-the-art algorithms for solving differential equations. The analysis and implementation of these algorithms will be discussed in some detail.
Content
Numerical Solution of Ordinary Differential Equations
Explicit Runge-Kutta methods. Order 4 conditions. Step size control. Convergence. Implementation.
Finite differences methods for partial differential equations
Elliptic problems in 1,2 and 3d, parabolic and hyperbolic problems in 1d. Convergence. Implementation.
Keywords
Explicit Runge-Kutta methods, elliptic, parabolic and hyperbolic pdes with finite difference methods.
Stability, converegence, implementation with matlab.
Learning Prerequisites
Recommended courses
Some background in numerical analysis and proficiency in programming - Matlab/Octave recommended
Important concepts to start the course
Numerical methods for approximation, differentiation and integration of functions. Basic knowledge of ordinary differential equations and their solutions. Basic knowledge of numerical techniques for solving systems of linear equations.
Learning Outcomes
By the end of the course, the student must be able to:
- Analyze methods
- Choose an appropriate method
- Prove basis properties of methods
- Derive new methods
- Conduct computational experiments
- Implement computational methods
Teaching methods
Lecture style with computational experiments in class to illustrate analysis.
Expected student activities
Students are expected to attend lectures and participate actively in class and exercises. Exercises will include both theoretical work and implementation and test of a variety of methods.
Assessment methods
Quizzes, graded homeworks 20%
Written examination 80%
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.
Resources
Bibliography
Lecture notes will be provided by the instructor. Complimentary reading:
Hairer, E.; Norsett, S. P.; Wanner, G. Solving ordinary differential equations. I. Springer, 1987.
Ressources en bibliothèque
Moodle Link
Dans les plans d'études
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Advanced numerical analysis II
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Advanced numerical analysis II
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Advanced numerical analysis II
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Advanced numerical analysis II
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Advanced numerical analysis II
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Advanced numerical analysis II
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel