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# Numerisk behandling av differentialekvationer II

## Under Construction 070104

Course responsible Jesper Oppelstrup jespero@nada.kth.se
Last course's homework problems: problemset 5, together with some useful lines in matlab (Hint for the analysis in problemset 5: consider constant u first), problemset 4, problemset 3, and problemset 2. Some improved hints on how to solve problemset 1.
There is an errata for the book (LeVeque: Finite Volume Methods for Hyperbolic Problems).

Find earlier displayed information here.

## About the Course

The course treats the numerical solution of differential equations. It emphasizes partial differential equations (PDE) solved by finite difference methods and finite volume schemes. Well-posedness, stability and other properties of schemes for hyperbolic systems of equations are a major concern, as well as elliptic and parabolic equations. The choice of boundary conditions has an impact on stability and well-posedness, and will be discussed. The goal of the course is to give students
1. Understanding of the mathematical concepts, properties and tools for analyzing differential equations and their discretizations, and ability to carry out the manipulations and calculations required.
2. Working knowledge and experience of implementing FD schemes with various boundary conditions
3. Experience of carrying out a complete solution of a computational problem - formulation, analysis, method choice, implementation, validation, and interpretation and presentation of results.
The theoretical part introduces model equations and Fourier - Continuous as well as Discrete - techniques for the analysis of equations and schemes. The theory is complemented by a set of homework, study problems, and computer labs on the formulation, analysis, and solution of model problems from engineering science. The students are expected to have a solid background of calculus, differential equations, and linear algebra; a basic course in numerical analysis is required, as is familiarity with the NADA computer environment and MATLAB.

## Instructors

Jesper Oppelstrup, `jespero@nada.kth.se`.
Mohammad Motamed, `mohamad@nada.kth.se`.
Office hours: by agreement.

## Literature

LeVeque: Finite Volume Methods for Hyperbolic Problems , Cambridge, 2002,

Other course materiel, such as

• homework problems,
• a set of examination questions

## CSC student office DELFI

Oscars Backe 2, level 2, open Mo-Fr 9.45-11.30, Mo-Thu 12.45-14.15, Tel: 790 8077.

## Examination

To pass the student must
1. Pass a written examination. (2 cred) The exam will consist of a selection of the distributed examination questions.
2. Solve the homework problems. (2 cred). Written reports of good quality must be handed in on given deadlines. You can find a latex file with a skeleton for a report in the course archive. Students will be asked to give a short oral presentation classroom-style of (parts of) the solutions.
3. Complete a project (1 cred) including classroom presentation.
For the problem sets the students are encouraged to work in groups of two, each group needs only to hand in one report, but the oral account is given individually. The project is also done in groups of two. All group members must be present at the presentation. The grade on the course will be based on the written examination, the homework solutions and the project. You do not need to register for the exam.

## Schedule

The schedule is available from KTH home page Time Edit "Schemagenerator". Lecture content plans will appear here shortly,
```2D1255 spring 07
Numerical Differential Equations II
D41       : Lindstedtsv. 17
D31,34    : Lindstedtsv. 5
E36,4V4Gul: Osquars B. 2

When         What    Where
==========================
Ons 17 jan 10  F1    D41
Tor 18 jan 10  F2    D41

Tis 23 jan 13  F3    D31

Tis 30 jan 13  F4    D31
Fre  2 feb 10 Lab    4V4Gul

Tis  6 feb 13  F5    D31
Fre  9 feb 13 Lab    4V4Gul

Tis 13 feb 13  F6    D41
Fre 16 feb 13 Lab    4V4Gul

Tis 20 feb 10  F7    D41
Fre 23 feb 13 Lab    4V4Gul

Tis 27 feb 10  F7    D41

Break

Tis 20 mar 10  F8    D31
Fre 23 mar 10 Lab    4V4Gul

Tis 27 mar 10  F9    D31
Fre 30 mar 10 Lab    4V4Gul

Tis 10 apr 10 F10    E36
Fre 13 apr 10 Lab    4V4Gul

Tis 17 apr 10 F11    E36
Fre 20 apr 10 Lab    4V4Gul

Tis 24 apr 10 F12    E36
Fre 27 apr 10 Lab    4V4Gul
13 Lab    4V4Gul

Tis  8 maj 13 F13    E36
Tor 10 maj 10 F14    D34
============================

Mån 21 maj 8:00-13:00 Exam B22, B23

```

## Registration and "course join" in RES

You must register with your Sektions Kansli to take this course. Please do so as soon as possible!. PhD students from other schools, please contact the course responsible ASAP.

You must also, as soon as you have decided to complete the course, register for participation in the CSC RES system. Homework, examination grades, etc., will be recorded and available to students ONLY in this way, and with some delay, in the web-based system "Mina Sidor". In the CSC unix system, upon login , do

``` res checkin ndiff2-07 ```

and

``` course join ndiff2-07 ```

When you have finished the course, exit the registration by

``` course leave ndiff2-07 ```

A course evaluation will be conducted via www from this home page, details to appear here shortly.

## Info directory

The course archive `/info/ndiff2-07` will probably stay empty, the stuff you need will be downloadable from this home page.

Upp till kursens hemsida.

Sidansvarig: Jesper Oppelstrup <jespero@nada.kth.se>
Senast ändrad 17 januari 2007