Numerical Solutions of Differential Equations
News
- 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 (katg@kth.se) 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!
Teachers
Responsible for the course and lecturer:
Katarina Gustavsson,
katg@kth.se.
Teaching assistant (lab instructor):
Davoud Saffar Shamshir Gar,
davoudss@kth.se.
Office hours: Wednesday 15-16 in room 206, Teknikringen 14, bottom floor.
Literature
Homework
There will be five homework sets.
- Homework 1 -- Check the
Demmel notes
for more about the matrix relation in 2.3 and
the Kronecker products in 2.4.
For the convergence parts, check the
notes on numerical convergence.
Deadline for Homework 1 is Monday 11 Feb, 2013
- Homework 2 -- Reading in Leveque:
Chaps. 2.7, 4-4.6, 7, 7.3.3, 13.1
Deadline for Homework 2 is Monday 11 Mars, 2013
- Homework 3 -- Reading:
Lecture notes 1,
Lecture notes 4,
Leveque:
Chap. 8.
Deadline for Homework 3 is Monday 8 April, 2013
- Homework 4 (new version) -- Reading in
Leveque: primarily Chaps 6 and 15.3-4 plus background in Chaps 11, 4.10-14, 12-12.1, 13. For the curious here are some
comments and discussions about exercise 2.2
Deadline for Homework 4 is Monday 29 April, 2013.
- Homework 5 -- Reading:
Lecture notes 5 , Lecture notes 6 and Lecture notes 7 . Homework 5 has a maximum of 4.0p.
Deadline for Homework 5 is Monday 20 May, 2013.
"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.
MERE SHEAVES OF MATLAB PLOTS, ONE TO A PAGE, WILL NOT BE ACCEPTED.
Matlab
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. |
Examination
To pass the course the student must
- Pass a written examination (3 ECTS).
-
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
| Score | 0-49 | 50-59 | 60-69 | 70-79 | 80-89 | 90-100 |
|---|
| Grade | F | E | D | C | B | A |
|---|
(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.
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