ndiff13

Numerical Solutions of Differential Equations
News
 The reexam will be in room E32.
 There will be a reexam on Thursday August 29 813. 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 1215.
 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 1315 in room 304 at Teknikringen 14.
 Lecture 1113 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, 1517 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 1012 in B23. Note that the schedule below is changed accordingly.
 The first lecture will be on Monday January 14, 2013, at 1012 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 1516 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, 44.6, 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 15.34 plus background in Chaps 11, 4.1014, 1212.1, 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 35 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
 emailing a link to Katarina where your or pdffiles can be downloaded, or
 emailing 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", CLEngineering 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 
10:0012:00 
Lecture 1 
B23 
Introduction to PDEs 
Lecture notes 1, Leveque 22.6 
5 
Wed 30 Jan 
13:0015:00 
Lecture 2 
B23 
Heat equation, wellposedness, properties, discretization 
Lecture notes 2, Leveque 44.2 

Fri 1 Feb 
15:0017:00 
Lab 1 
Sport 
Work with homework 1 

6 
Mon 4 Feb 
10:0012:00 
Lecture 3 
B23 
Heat equation, discretization, properties of discretization, Matlab hints 
Lecture notes 3,
Matlab notes (Lindbo, Getreuer) 

Thu 7 Feb 
15:0017:00 
Lab 2 
Sport 
Work with homework 1 


Tue 12 Feb 
10:0012:00 
Lecture 4 
B23 
Hyperbolic equations, intro, characteristics 
Leveque 2.72.11 (2.122.14), 33.6, 99.1 
8 
Mon 18 Feb 
10:0012:00 
Lecture 5 
B23 
Hyperbolic equations cont.,
discontinuous solutions, boundary conditions,
basic discretizations 
Leveque 3.73.11, 44.1, 4.54.9, 7 

Tue 19 Feb 



Deadline homework 1 


Fri 22 Feb 
15:0017:00 
Lab 3 
Sport 
Work with homework 2 

9 
Wed 26 Feb 
10:0012:00 
Lecture 6 
B23 
Convergence theory for linear methods 
Leveque 4.34.4, 88.3.4, Lecture notes 4 
11 
Mon 11 Mar 



Deadline homework 2 

12 
Mon 18 Mar 
08:0010:00 
Lecture 7 
B23 
Convergence theory for linear methods cont.,
errors for discontinuous solutions 
Leveque 8.68.7, Lecture notes 4 
13 
Mon 25 Mar 
08:0010:00 
Lecture 8 
B23 
Nonlinear hyperbolic equations 
Leveque 1111.13 

Tue 26 Mar 
13:0015:00 
Lab 4 
Sport 
Work with homework 3 

15 
Mon 8 Apr 



Deadline homework 3 


Thu 11 Apr 
15:0017:00 
Lecture 9 
B23 
Finite volume methods for nonlinear hyperbolic equations, Godunov, Riemann problems, approximate Riemann solvers 
Leveque 3.83.9, 4.104.14, 1212.1, 12.9, (13.213.12 no details), 15.1, 15.315.3.3 
16 
Wed 17 Apr 
13:0015:00 
Lecture 10 
B23 
High resolution methods, total variation, slope and flux limiters 
Leveque 66.15, 12.8, 12.10, 15.4 

Fri 19 Apr 
15:0017:00 
Lab 5 
Sport 
Work with homework 4 

17 
Tue 23 Apr 
13:0015:00 
Lecture 11 
304 
Boundary integral methods for elliptic problems. Rikard Ojala 
Lecture notes 5 
18 
Mon 29 Apr 



Deadline homework 4 


Tue 30 Apr 
13:0015:00 
Lecture 12 
B23 
Boundary integral methods for elliptic problems. Rikard Ojala 
Lecture notes 6 
19 
Tue 7 May 
13:0015:00 
Lecture 13 
B23 
Boundary integral methods for elliptic problems. Rikard Ojala 
Lecture notes 7 
20 
Mon 13 May 
13:0015:00 
Lab 6 
Sport 
Work with homework 5 

21 
Mon 20 May 



Deadline homework 5 

21 
Fri 24 May 
08:0013:00 
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 35 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  049  5059  6069  7079  8089  90100 
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 57).
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
Rappserver.
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.
