Numerical methods for ODE
This course is given at graduate level and corresponds to 7.5 hp. The goal is to give an overview of important techniques and concepts related to numerical integration of ODEs (convergence, stiffness, adaptivity), but also to discuss in detail some techniques. In particular we will consider linear multistep methods and Runge-Kutta methods, and discuss methods that preserve important invariants.
News:
The schedule is updated. Until further notice the lectures will be given online
Literature:
Dq Dahlquist lecture notes : http://user.it.uu.se/~perl/ODE_07/NumODEsbook.pdf
HNW Hairer, Nørsett, Wanner: Solving Ordinary Differential Equations I (2nd ed), Springer
HW, Hairer, Wanner: Sollving Ordinary Differential Equations II (2nd ed), Springer
HWL, Hairer, Wanner, Lubich, Geometric Numerical Integration, Springer
Teacher:
First lecture: Tuesday Sept 8, 13.15-15, room 2344
outline of the course:
| date&time | room | topic | reading | problem set | |
|---|---|---|---|---|---|
| 1 | Sept 8, 13-15 | 2344 | Introduction and discussion of mathematical background of ODEs | Dq p1-34 | Dq pp35: P4,P8,P13, Dq pp88: P2 and P8, due October 2 |
| 2 | Sept 15, 13-15 | 2344 | one-step methods, convergence, stability, stiffness, adaptivity | Dq p52-76 | |
| 3 | Oct 1, 13-15 | 2344 | continued | ||
| 4 | Oct 8, 10-12 | 2344 | linear multistep methods | HNW III.2 and III.4, Dq p116-122 | Dq pp127-128: problems 3,5,10 due October 28 |
| 5 | Oct 15, 13-15 | 2344 | more on linear multistep methods | ||
| 6 | Nov 5, 13-15 | 2344 | implementational issues | ||
| 7 | Nov 12, 13-15 | 2344 | Runge-Kutta methods | ||
| 8 | Nov 19, 13-15 | 2344 | more on RK | HNW II.1-5, HW IV.2,.3,.6,.15 |
problem set 3, due November 30 |
| 9 | Nov 25 15-17 | 2344 | symplectic methods,preservation of invariants | HNWp312-337, HWLp179-191,237-245 |
problem set4, due December 18 |
| 10 | Dec 4, 10-12 | 2345 | continued | ||