Up to *kursens hemsida*.

# Recent information on 2D5234, (DN3234) Numerical Methods for ODEs and DAEs

## Schedule

September 17, 10-17, Uppsala, Polacksbacken, room 2345

October 1, 10-17, KTH, huvudbyggnad, room 4523

October 15, 10-17, Uppsala, Polacksbacken, room 2345

October 26, 10-17, KTH, huvudbyggnad, room 1635

Lunch break 12-13

**The starting date is September 17 in Uppsala.**
## Lecturer

The lecturer at KTH is
Michael Hanke,
`hanke@nada.kth.se`

.
The lecturer in Uppsala is Per Lötstedt with e-address
`perl@it.uu.se`

## Literature

G. Dahlquist, Numerical Methods for Ordinary Differential Equations, lecture notes.

P. Deuflhard, F. Bornemann, Scientific Computing with Ordinary
Differential Equations, Springer, 2002.

E. Hairer, S. P. Nørsett, G. Wanner, Solving Ordinary Differential
Equations, Vol I, Springer, 1993.

E. Hairer, G. Wanner, Solving Ordinary Differential
Equations, Vol II, Springer, 1996.

## Contents

Part I (September 17, Uppsala)
Some background in ODEs, 2h

One-step methods, convergence, stability, stiffness, 2h

Errors, adaptivity, 2h

Part II (October 1, KTH)

Runge-Kutta methods, accuracy conditions, stability, 4h

Preservation of invariants, symplectic methods, 2h

Part III (October 15, Uppsala)

Linear multistep methods, BDF methods, errors, stability, 4h

Implementation issues, 2h

Part IV (October 26, KTH)

Differential-algebraic equations (DAEs)

Sources of DAEs including singular perturbation problems, CMBS, electrical
networks, method of lines for systems of PDEs, theory, 2h

numerical methods, asymptotic stability, 4h

Here you'll find some additional reading on DAEs:

## Homework assignments

After each 6h-lecture there will be homework assignments solve on the material
covered by the lecture.
- First homework: Problems in Dahlquist's lecture notes:
Problems P6a-f on page 38 in Dahlquist's lecture notes, P7a-c on page 39, P11
on page 41, P7 on page 89, let the matrix be the tridiagonal matrix with 2 on the diagonal and
-1 on the subdiagonal and the superdiagonal, P8 on page 89.
- Homework 2
- Third homework: Problems in Dahlquist's lecture notes: P3 on p 127, P5 on p 127,
P7 on p 128, P10 on p 128.
- Homework 4

## Examinations

Here you can download the final examination project.
In case that you have your own project you are welcome to solve this.
Please contact the course leader (Per Lötstedt in Uppsala or Michael Hanke
at KTH) for approval before starting your own project!
Up to *kursens hemsida*.

Responsible for this page: Michael Hanke <hanke@nada.kth.se>

Latest change August 17, 2011

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