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# Numerisk behandling av differentialekvationer II

## Latest News

EXAM: Feb 6 2006, 8-13. You must register for the exam by sending an email to`gunillak@nada.kth.se`.

The schedule has been updated. See below.

The last problemset: Problem set 7. Find Problem set 6, Problem set 5, Problem set 1, problem set 2, problem set 3, problem set 4. Note that problem set 4 should be handed in no later than March 10. Corrected reports can be collected during office hour.
There is a set of possible exam quastions.
Find earlier displayed information here.

The course treats the numerical solution of differential equations. It emphasizes partial differential equations (PDE) and finite difference methods and finite volume schemes. Well-posedness, and stability and 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 and study problems, computer labs, and a larger project on the formulation, analysis, and solution of a "realistic" problem. 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.

## Teacher

Teacher is Gunilla Kreiss, `gunillak@nada.kth.se`.
Assistant: Mohammad Motamed, `mohammad@nada.kth.se`.
Office hours: Wednesdays and Fridays 13-14.

## Literature

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

Other course materiel, such as

• homework problems,
• a set of examination questions
will be distributed on lectures and shown under latest news.

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 8 homework problems. 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.
For the problem sets the students are encouraged to work in groups of two (not three), each group needs only to hand in one report. The grade on the course will be based on the written examination. The written exam is scheduled to Tuesday May 30 8.00-13.00 in rooms Q11 and Q12. You do not need to register for the exam.

## Schedule

• 20 Jan, 13-15, Lecture 1 in M32
Introduction, theory and numerical methods for methods ODE.
• 24 Jan, 13-15, Lecture 2 in D34
Conservation Laws, chapter 2 of book.
• Jan 27, 13-15 Lecture 3 in M32
More about conservation Laws, chapter 3 of book.
• 31 Jan, 13-15, Lecture 4 in D34
Finite Volume methods, ch 4.
• 3 Feb, 13-15, Lecture 5 in M32,
Boundary Conditions, Ch 7
• 7 Feb, 8-10, Computer session 1, in yellow computer room,
Work with problem set 2
• 10 Feb, 13-15, Lecture 6 in M32
wellposedness of time dependent PDEs
• 14 Feb, 13-15, Computer session in yellow,
problem set 3
• 17 Feb, 13-15, Lecture 7, M32
Stability theory for numerical methods, ch 8,
• 21 Feb, 13-15, Computer session in yellow,
problem set 3
• 24 Feb, 13-15, Lecture 8 in M32
higher order methods for non-linear scalar scalar conservation laws, ch 6, ch 12
• 1 Mar, 13-15, Computer session, red
problem set 4
• 5 Apr, 15-17, Lecture 9 in D31
High order methods for PDEs with smooth solutions
• 7 Apr, 15-17, Computer session in yellow,
problem set 4
• 12 May, 15-17, Lecture 10 , D31
Summation-By-Parts operators and implementation of boundary conditions
• 14 Apr, 15-17, Computer session in yellow,
problem set 5
• 19 Apr, 15-17, Lecture 11 in D31
Scalar Hyperbolic problems in 2D, FV methods
• 21 Apr, 13-15, Computer session, ?
problem set 5
• 26 Apr, 15-17, Lecture 12 in D31
System of Hyperbolic equations in 2D, boundary conditions
• 3 May, 15-17, Lecture 11 in D31
Numerical approximations of Parabolic problems,
• 6 May, 15-17, Computer session, yellow
problem set 6
• 10 May, 15-17, Lecture 12 in D31
• 12 May, 13-15, Computer session, yellow
problem set 7, yellow
• 17 May, 13-15, Lecture 13 in D31
Last lecture
• 19 May, 13-15, Computer session, yellow
problem set 7
• 30 May, EXAM, in Q11, Q12
The schedule for the 4th period will be distributed later.

## Registration och "course join"

You must regiter with your Sektions Kansli to take this course. Please do so as soon as possible!

You should also give the commands

``` res checkin ndiff2-06 ```

and

``` course join ndiff2-06 ```

when logged in. When you have finished the course, write

``` course leave ndiff2-06 ```

You do not need to register for the exam.

## Info directory

There is a course archive: `/info/ndiff2-06`.

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