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Information on 2D1255,
Numerisk behandling av differentialekvationer II
Latest News
EXAM: Feb 6 2006, 813. You must register for the exam by sending an email togunillak@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.
About the Course
The course treats the numerical solution of differential
equations. It emphasizes partial differential equations (PDE) and
finite difference methods and finite volume schemes. Wellposedness, 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 wellposedness, and will be discussed.
The goal of the course is to give students
 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.
 Working knowledge and experience of implementing FD
schemes with various boundary conditions
 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 1314.
Literature
LeVeque: Finite Volume Methods for Hyperbolic Problems
, Cambridge, 2002,
Other course materiel, such as
 homework problems,
 a set of examination questions
 additional material and reading hints,
will be
distributed on lectures and shown under latest news.
NADAS student office
Oscars Backe 2, level 2, open MoFr 9.4511.30, MoThu 12.4514.15,
Tel: 790 8077.
Examination
To pass the student must
 Pass a written examination. (2 cred) The exam will consist of a
selection of the distributed examination questions.
 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 8.0013.00 in rooms Q11 and
Q12.
You do not need to register for the exam.
Schedule
 20 Jan, 1315, Lecture 1 in M32
Introduction, theory and numerical methods for methods ODE.

24 Jan, 1315, Lecture 2 in D34
Conservation Laws, chapter 2 of book.

Jan 27, 1315 Lecture 3 in M32
More about conservation Laws, chapter 3 of book.

31 Jan, 1315, Lecture 4 in D34
Finite Volume methods, ch 4.

3 Feb, 1315, Lecture 5 in M32,
Boundary Conditions, Ch 7

7 Feb, 810, Computer session 1, in yellow computer room,
Work with problem set 2

10 Feb, 1315, Lecture 6 in M32
wellposedness of time dependent PDEs

14 Feb, 1315, Computer session in yellow,
problem set 3

17 Feb, 1315, Lecture 7, M32
Stability theory for numerical methods, ch 8,

21 Feb, 1315, Computer session in yellow,
problem set 3

24 Feb, 1315, Lecture 8 in M32
higher order methods for nonlinear scalar scalar conservation laws, ch 6, ch 12

1 Mar, 1315, Computer session, red
problem set 4

5 Apr, 1517, Lecture 9 in D31
High order methods for PDEs with smooth solutions

7 Apr, 1517, Computer session in yellow,
problem set 4

12 May, 1517, Lecture 10 , D31
SummationByParts operators and implementation of boundary conditions

14 Apr, 1517, Computer session in yellow,
problem set 5

19 Apr, 1517, Lecture 11 in D31
Scalar Hyperbolic problems in 2D, FV methods

21 Apr, 1315, Computer session, ?
problem set 5

26 Apr, 1517, Lecture 12 in D31
System of Hyperbolic equations in 2D, boundary conditions

3 May, 1517, Lecture 11 in D31
Numerical approximations of Parabolic problems,

6 May, 1517, Computer session, yellow
problem set 6

10 May, 1517, Lecture 12 in D31
more about Parabolic problems,timescales etc

12 May, 1315, Computer session, yellow
problem set 7, yellow

17 May, 1315, Lecture 13 in D31
Last lecture

19 May, 1315, 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 ndiff206
and
course join ndiff206
when logged in.
When you have finished the course, write
course leave ndiff206
You do not need to register for the exam.
Info directory
There is a course archive:
/info/ndiff206
.
Upp till kursens hemsida.
Sidansvarig: Gunilla Kreiss <gunillak@nada.kth.se>
Senast ändrad 16 januari 2006
Tekniskt stöd: <webmaster@nada.kth.se>