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KTH / CSC / Kurser / DN2255 / ndiff13

Numerical Solutions of Differential Equations


  • The re-exam will be in room E32.
  • There will be a re-exam on Thursday August 29 8-13. Please contact,
    before August 12, Katarina ( if you plan to attend the exam.
    Room will be anounced later.

  • The exam is now graded and the results have been reported. You should be able to
    check the result at "Mina Sidor". Graded exams can be collected at the
    Math Student Expedition, Lindstedtsvägen 25, open every day between 12-15.

  • Slides from the third lecture on Boundary Integral methods by Rikard Ojala.

  • You can now find homework 5 under the Homework section.
  • Slides from the second lecture on Boundary Integral methods by Rikard Ojala.

  • Extra lab on Friday 26 April at 15.00 in Sport.
  • Slides from the first lecture on Boundary Integral methods by Rikard Ojala.

  • Homework 4 is updated with some corrections. Please download the new version.

  • Lecture 11 (24/4) is moved to 23/4 13-15 in room 304 at Teknikringen 14.
  • Lecture 11-13 will be given by a guest lecturer: Rikard Ojala.
    The topic will be Boundary integral methods for elliptic problems

  • We need to move the lecture on Wednesday April 24, to either Tuesday April 23 or
    Friday April 26. We will descide in class on Thursday April 11.
  • You can now find homework 4 under the Homework section.

  • There will be an extra lab session on Friday, March 1, 15-17 in Sport.

  • Now, I have updated the deadlines for the homework, see the schedule.
  • You can now find homework 2 under the Homework section.
    There you will also find "the rules" regarding homework deadlines.

  • The first lecture was unforunatly cancelled. We will instead start on Wednesday January 23, 2013,
    at 10-12 in B23. Note that the schedule below is changed accordingly.
  • The first lecture will be on Monday January 14, 2013, at 10-12 in B23. Welcome!


Responsible for the course and lecturer:

Katarina Gustavsson,

Teaching assistant (lab instructor):

Davoud Saffar Shamshir Gar,
Office hours: Wednesday 15-16 in room 206, Teknikringen 14, bottom floor.



There will be five homework sets.

"Rules" regarding the homework deadlines

The homework is graded and each set gives a maximum of 3-5 points. Homeworks handed in no later than
  • the deadline: full points if everyting is correct + the option to hand in smaller correction (to increase the number of points) within a week after the graded homework is handed out.
  • one week after the deadline: obtained points will be reduced by 0.5 points and there is no option to hand in corrections.
For homeworks handed in later than one week after the deadline: obtained points will be reduced by 1.5 points and there is no option to hand in corrections.

Please have in mind that in order to "pass" the homework part of the course, you must obtain at least half of the total points on each homework.

How to hand in reports

Reports MUST have a cover page with author names, course code (DN2255) and homework number, and instructor name. The reports can be handed in by
  • e-mailing a link to Katarina where your or pdf-files can be downloaded, or
  • e-mailing Katarina that a paper version has been deposited in NA mailbox, bottom floor, Teknikringen 14 (outside corridor)
  • Add Matlab code as an appendix to the report.

Obs! Please do not email your full reports! This will rapidly fill up my mailbox.

For plots in your report, make sure you

  • label axes correctly
  • explain what the plots show
  • combine plots so that comparisons are easy.


The exercises will require Matlab programming. Students are expected to have procured familiarity with this environment in previous courses. Here are some notes on writing well structured and efficient Matlab programs: Here are some reading tips for students who feel less comfortable with the Matlab environment:
  • Chapman, "MATLAB Programming for Engineers", CL-Engineering 2007
  • Moler, "Numerical Computing with Matlab", SIAM 2004

Lecture and Computer Lab Schedule

The course has 13 lectures, and 6 supervised computer exercise classes.

Week Date Time Class
Room Topics Reading
4 Wed 23 Jan 10:00-12:00 Lecture 1 B23 Introduction to PDEs Lecture notes 1, Leveque 2-2.6
5 Wed 30 Jan 13:00-15:00 Lecture 2 B23 Heat equation, well-posedness, properties, discretization Lecture notes 2, Leveque 4-4.2
Fri 1 Feb 15:00-17:00 Lab 1 Sport Work with homework 1
6 Mon 4 Feb 10:00-12:00 Lecture 3 B23 Heat equation, discretization, properties of discretization, Matlab hints Lecture notes 3, Matlab notes (Lindbo, Getreuer)
Thu 7 Feb 15:00-17:00 Lab 2 Sport Work with homework 1
Tue 12 Feb 10:00-12:00 Lecture 4 B23 Hyperbolic equations, intro, characteristics Leveque 2.7-2.11 (2.12-2.14), 3-3.6, 9-9.1
8 Mon 18 Feb 10:00-12:00 Lecture 5 B23 Hyperbolic equations cont., discontinuous solutions, boundary conditions, basic discretizations Leveque 3.7-3.11, 4-4.1, 4.5-4.9, 7
Tue 19 Feb Deadline homework 1
Fri 22 Feb 15:00-17:00 Lab 3 Sport Work with homework 2
9 Wed 26 Feb 10:00-12:00 Lecture 6 B23 Convergence theory for linear methods Leveque 4.3-4.4, 8-8.3.4, Lecture notes 4
11 Mon 11 Mar Deadline homework 2
12 Mon 18 Mar 08:00-10:00 Lecture 7 B23 Convergence theory for linear methods cont., errors for discontinuous solutions Leveque 8.6-8.7, Lecture notes 4
13 Mon 25 Mar 08:00-10:00 Lecture 8 B23 Nonlinear hyperbolic equations Leveque 11-11.13
Tue 26 Mar 13:00-15:00 Lab 4 Sport Work with homework 3
15 Mon 8 Apr Deadline homework 3
Thu 11 Apr 15:00-17:00 Lecture 9 B23 Finite volume methods for nonlinear hyperbolic equations, Godunov, Riemann problems, approximate Riemann solvers Leveque 3.8-3.9, 4.10-4.14, 12-12.1, 12.9, (13.2-13.12 no details), 15.1, 15.3-15.3.3
16 Wed 17 Apr 13:00-15:00 Lecture 10 B23 High resolution methods, total variation, slope and flux limiters Leveque 6-6.15, 12.8, 12.10, 15.4
Fri 19 Apr 15:00-17:00 Lab 5 Sport Work with homework 4
17 Tue 23 Apr 13:00-15:00 Lecture 11 304 Boundary integral methods for elliptic problems. Rikard Ojala Lecture notes 5
18 Mon 29 Apr Deadline homework 4
Tue 30 Apr 13:00-15:00 Lecture 12 B23 Boundary integral methods for elliptic problems. Rikard Ojala Lecture notes 6
19 Tue 7 May 13:00-15:00 Lecture 13 B23 Boundary integral methods for elliptic problems. Rikard Ojala Lecture notes 7
20 Mon 13 May 13:00-15:00 Lab 6 Sport Work with homework 5
21 Mon 20 May Deadline homework 5
21 Fri 24 May 08:00-13:00 Exam E33 All of the above All of the above, except the Matlab notes.


To pass the course the student must
  1. Pass a written examination (3 ECTS).
  2. Solve the five homework problems (4.5 ECTS).
    For each homework set a written report of good quality should be handed in. The students are encouraged to work in groups of two. The homework is graded and each set gives a maximum of 3-5 points, in total at most 21 points for all five sets. A homework problem is considered as "solved" if at least half of the maximum points are given.

Final grade

The final grade of the course is based on the results of the homework (60%) and the written examination (40%). More precisely, the final score is between 0 and 100, given by the formula:

Score = Exam points + Homework points * 60/21.

The preliminary grading scale is


(Subject to minor modifications.)

Exam hints

Exam questions will cover the reading material (see table above) as well as the homework material. There will be no exam questions on Matlab, however. The style of the exam will be as earlier years, exemplified by: Note that the contents of the course have shifted slightly over the years, so unlike in some of the old exams, there will not be questions on e.g. spectral methods, multigrid and stiff source terms. On the other hand, there may be questions on boundary integral methods (based on lecture notes 5-7).

Course activation in Rapp

For registration to the course, please contact your "kansli"/"studievägledning"/coordinater. Once registered, for us to be able to report your results on the course you need to show that you are active in our reporting system Rapp.

This you can do by connecting to Rapp-server.

Click on Logga in / Log in. You will be forwarded to KTH's login page where you can log in with your usual KTH username/password.

Copyright © Sidansvarig: Katarina Gustavsson <>
Uppdaterad 2013-08-15