TMA4212 Numerical solution of differential equations by difference methods

The solution to the exam is available on It's learning.
Permitted examination support material: C: Approved simple pocket calculator is allowed. Rottman is allowed.
You should prepare to the exam assuming that no aids are allowed.
Important! Remember the final deadline for handing in compulsory exercises: April 24th. You need to have all four exercises approved to take the final exam. You can check the status of your exercises on
To hand in the project, send your report (in pdf, please) and matlab files by mail to Lars within the deadline. Remember to include instructions on how to run your program.
The project presentations are scheduled Monday March 7 12:15-15:00 in F6 (notice the extra hour). It is compulsory for everyone to participate. Each group should prepare a presentation of maximum 10 minutes where you should give an overview of the work done. Be honest, the main goal is to allow us (Elena, Lars og Jon Vegard) to give you useful feedback towards the optimal conclusion of the project work and report. To save time between the presentations, send your presentation by mail to Lars by 10:00 on Monday.
Notice that there are no supervision today (Thursday March 3) since we will use the lecture hours tomorrow. However, for those that were not able to attend yesterday, Lars will be available at his office 13:15-14:00 today.
Elena is sick today (Wednesday), so she will not be available in the office hours. However, as announced before, there will be supervision in Nullrommet today 12:15-14:00.
All of the compulsory exercises have now been evaluated. You should check if yours are approved here: Note that you need to have all exercises approved in order to take the final exam. If you have any rejected exercises, you need to follow the feedback given and resubmit the exercise by mail to Lars. Because of the project work you are given the opportunity to do this after easter. The absolute final deadline for handing in is April 24th!
The hours for project supervision for the next three weeks has been updated. This week, there will be supervision both Wednesday and Thursday, and the week after we will use both lecture hours for supervision in addition to Wednesday.
There will be no lecture Friday February 19th. Instead, there will be supervision of the project in Nullrommet 12:15-14:00.
Dear students, today 11th of February 2016 I forgot that I promised to come to the usual supervision class on Thursday to help you with your homework. I apologize, this just totally escape my mind and I'm very sorry for this. Tomorrow 12th of February 2016, Jon Vegard will be in Nullrommet for supervisions starting from 14:15.
The new deadline for all the homework is Sunday February 14th. The last deadline to a make a group for the project work and choose a PDE is also Sunday February 14th. Please check the Registration form in under "Registration", to see if your group is registered there. If you do not find yourselves, you need to take action and register your group. We recommend everybody to start working on the project as soon as possible. There is now less than one month to the day of the project presentation (March 7th), soon after that many students will leave for the excursion. If you do not start soon working with the project, you will not be able to finish the necessary work in time. These are going to be though working times for you guys, but that is the price you pay to be done with the project before Easter, and there will be much less (programming) work for you after Easter. Good luck with the project!
This week (February 8th to 12th) and until the 17th of February, Lars is on parental leave. I will cover homework supervision on Thursday 11th from 13 to 14 (I will try to be there before 13, if I can make it). Jon Vegard will supervise on Friday 12th from 14:15.
Jon Vegard cannot be at the supervision today 12-14, because of collision with some other teaching duties. The supervision today is shorter, I will cover this supervision from 12-13. Jon Vegard will be available for supervisions on Friday 5th of February from 14:15 and on Friday 12th of Feberuary from 14:15.
Lars is on parental leave for two weeks. Jon Vegard Venås will supervise your homework and be available during the office hours (Wednesdays 13-14) during these two weeks. Please send your e-mails to Elena or Jon Vegard, Lars will not answer e-mails in these two weeks.
Starting from this week both Lars and Elena will have office hours on Wednesdays from 13:15-14. Please note that the office hours might be changed.
Homework 1 has been corrected, visit to see if your have been approved. Under Homework, you will find a list of the most common errors. You should check if any of these apply to you.
The project page is updated with additional information. In particular, you will find a registration form to register your group. For those of you that are alone or in pairs, you are given the option of joining an available group, see instructions. Once you have registered your group, send a mail to Lars with a prioritized list of three PDE's (first come, first served).
The exercise class has been rescheduled to Thursday 12:15-14:00 (still in Nullrommet). Be aware that if there are no students present at 13:00 I will leave. For those of your that are not able to attend at this time, Lars will be available at his office Wednesday 13:15-14:00. There might be changes to this plan when the project starts.
Please answer the doodle poll by this weekend. We will use this information to try to reschedule the exercise class and to set up supervision hours for the project.
The weekly exercise classes will be held in Nullrommet. If you don't have access to Matteland, you need to send your full name, NTNU username and the card number on your student identity card to Lars as soon as possible.
The first exercise set is available under Homework.
We will try to reschedule the weekly exercise class. Please answer this doodle poll by Thursday January 14. The exercise class this week will be Thursday 18-19.
First lecture 11th of January 2016 12:15-14:00 in F6
Important dates
First lecture: Monday 11th of January 2016.
Choose the PDE for the project: 1st of February.
Presentation of the project: 7th of March.
Project deadline: 17th of March.


  • Everything in the note (a part what specified in Timetable).
  • Chapters of the books as specified under Timetable.
  • All old exam questions (as detailed in old exams).
  • All the exercise sets given as Homework.


F6 Mondays and Fridays 12-14

Nullrommet, 3rd floor, central building 2 (Sentralbygg 2), Thursdays 12-14


Description of the course

In the following link you can find detailed information about the course, the main topics presented and the learning outcome.


Learning outcome in itemized form:

Code Description
Knowledge L1 Understanding of error analysis of difference methods: consistency, stability, convergence of difference schemes.
L2 Understanding of the basics of the finite element method.
Skills L3 Ability to choose and implement a suitable discretization scheme given a particular PDE, and to design numerical tests in order to verify the correctness of the code and the order of the method.
L4 Ability to analyze the chosen discretization scheme, at least for simple PDE-test problems.
L5 Ability to attack the numerical linear algebra challengies arizing in the numerical solution of PDEs.
General competence L6 Ability to present in oral and written form the numerical and analytical results obtained in the project work.
L7 Ability to apply aquired mathematical knowledge in linear algebra and calculus to achieve the other goals of the course.


Elena Celledoni, room 1346 Sentralbygg II.

Exercise and project lecturer

Lars Hov Odsæter, room 1340, Sentralbygg II.

Jon Vegard Venås, room 1338, Sentralbygg II.

Reference group

  • Master in mathematics: Abdul Ghaffar Rehman Malik agmalik (at)
  • Industrial mathematics: Siri Narvestad Fatnes sirinf (at)
  • Industrial mathematics: Markus Brabrand Urfjell markusbrabrandurfjell (at)

Office hours

Office hours for Lars and Elena:

Day Hour

Please note that the office hours might be changed.

Elena will not be available for office hours on the 17th of February.

Exercises and project

The exercises and exercise classes in this course are mostly aimed at facilitating the work for the project. Both lectures and exercises classes are also a preparation to the exam (in terms of exam exercises). The exercise classes make use of computers and will be held in NULLROMMET starting from the 14th of January.

The project aims at developing experience in implementing and experimenting with finite difference discretizations of PDEs. This is the core of this course. It contributes to achive the following goals for the course: L1, L3, L4, L5, L6, L7. The project is divided in two tasks (implementation and analysis) which can be viewed as two separate exercises. Refer to the official description of the course for the requirements on project/exercises relative to the exam. The project work is essential to achieve L3, L5, L6 (which is about 40 % of the learning outcome for the course). See the project description for more detalied information.

Teaching material

Evaluation system and marking in this course
  1. The exercises count for 5% the final mark and are compulsory.
  2. The project counts for 35 % of the final mark.
  3. The final exam counts for 60 %. You must pass the final (written) exam to pass this class (project + homework + final exam).
  4. You get credit only for project work and exercises made during this semester.
  5. The total mark is the only official mark for the course. The marking of the project is unofficial and will be published on It's learning (in letter form: A,B,C,D,E,F).
2016-05-28, Elena Celledoni