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Department of Information Technology

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.


The schedule is updated. Until further notice the lectures will be given online


Dq Dahlquist lecture notes :
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


Gunilla Kreiss

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
Updated  2020-12-06 18:05:37 by Gunilla Kreiss.