MMF910 Numerical methods for ODEs Spring 24
This PhD-level course is about numerical methods for solving ordinary differential equations. In addition to standard theory, such as convergence results etc., I shall put some emphasis on geometric structures and how to preserve them in the numerical solution (cf. geometric numerical integration).
The course comprises:
- lectures/exercise sessions (about one per week),
- mandatory exercises (to be handed in via Canvas),
- individual course projects, handed in as a report and presented in class.
Suitable, general literature (more specific reading material will be given during the lectures and in the exercises):
- [HLW-2006] Hairer, Wanner, and Lubich: Geometric Numerical Integration, Springer (2006)
- [MQ-2006] McLachlan and Quispel: Geometric integrators for ODEs, J. Phys. A 39 (2006)
Program
The lectures are on Tuesdays at 13:15 in MV:H11, except:
- 6/2, which is left for self-studies since I'm in Pisa the whole week;
- 13/2, where instead there is the licentiate presentation of Michael Roop at 10:00 in room Pascal.
Lectures
| Day | Content | |
|---|---|---|
| 16/1 | Prequel to numerics: from Kepler to Poincaré | |
| 23/1 | Basic ODE theory and ODE numerics | |
| 30/1 | Convergence of numerical integrators | |
| 6/2, 13/2 | Self-studies: Chapter II of [HLW-2006] | |
| 20/2 | Review of integrators and symplecticity | |
Exercises
| Week | Exercises |
|---|---|
| 1 | Read the paper "Kepler, Newton and numerical analysis". |
| 2 | Local existence and uniqueness |
| 3-4 | Convergence of the implicit midpoint method |
| 4-5 | Runge-Kutta exercises |
| 6 | Symplectic experiments |
Course summary:
| Date | Details | Due |
|---|---|---|