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Information on ndiff2-07,

Numerisk behandling av differentialekvationer II

Latest News

070904

Re-examination prel. planned for September 25. Please register by e-mail to jespero@nada.kth.se; suggest other time, if sep 25 is not suitable.

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Under Construction 070118


Under Construction 070104


Course responsible Jesper Oppelstrup jespero@nada.kth.se
Last course's homework problems: problemset 6, 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

will be distributed on lectures and downloadable from this home page.

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 below. 
2D1255 spring 07
Numerical Differential Equations II
                     D41       : Lindstedtsv. 17
                     D31,34    : Lindstedtsv. 5			
                     E36,4V4Gul: Osquars B. 2
Lecture plan
When              Where   What                        Ref.
=======================================================================
Wed 17 Jan 10 F1  D41 Intro., theory & num. methods ODEs 	From 2D1225
Thu 18 Jan 10 F2  D41 Cons. laws, FV for Parabolic PDEs 	Ch.2.1-5,4.1-2

Tue 23 Jan 13 F3  D31 Multigrid  				Extra material
 
Tue 30 Jan 13 F4  D31 Hyperbolic conservation laws		Ch.3
Fri  2 Feb 10 L1  4V4Gul
 
Tue  6 Feb 13 F5  D31 Fin. Vol. for hyperbolic cons.laws	Ch.4 and 6
Fri  9 Feb 13 L2  4V4Gul
 
Tue 13 Feb 13 F6  D41 BC for hyp.systems, well-posedness  Ch.7, Extra 
Fri 16 Feb 13 L3  4V4Gul
 
Tue 20 Feb 10 F7  D41 Convergence, Accuracy, Stability	Ch.8
Fri 23 Feb 10 Fx  K51 F7, cont'd
Fri 23 Feb 13 L4  4V4Gul
 
(Tue 27 Feb 10 F8  D41) More about von Neumann analysis - canceled
---- changed to ----
Tue 27 Feb 15 F8  D32 More about linearization, freezing of coefficients, etc.

Break
 
(Tue 20 Mar 10 F9  D31) High resolution I, canceled 			Ch.6,10
---- changed to ----
Mon 19 Mar 15 F9  4523  High resolution I, Lab 3		Ch.6,10
Fri 23 Mar 10 L5  4V4Gul
 
(Tue 27 Mar 10 F10 D31) canceled
---- changed to Tue, April 10 ----
Fri 30 Mar 10 L6  4V4Gul
 
Tue 10 Apr 10 F11 E36 Nonlinear hyperbolic 			Ch.11
Tue 10 Apr 13 F11 E36 High resolution II 			Ch.12
Fri 13 Apr 10 L7  4V4Gul
 
Tue 17 Apr 10 F12 E36 Hyperbolic Problems in multiD	Ch.18,19
Fri 20 Apr 10 L8  4V4Gul
 
Tue 24 Apr 10 F13 E36 Boundary conditions in multiD
Fri 27 Apr 10 L9  4V4Gul
           13 L10 4V4Gul

Tue  8 May 13 F14 E36 Non-reflecting boundary conditions	Extra
Thu 10 May 10 F15 D34 Projects, review
==============================================================

Mån 21 May 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.

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Sidansvarig: Jesper Oppelstrup <jespero@nada.kth.se>
Senast ändrad 4 september 2007
Tekniskt stöd: <webmaster@nada.kth.se>