Time Integration of PDEs

Time integration of PDEs, Summer 2016

Current announcements

  • The schedule for the oral exams is now available and can be found here.
  • The Q&A-session tomorrow is hold in a different room: at 9:45 at room 3.061.
  • The deadline for registering for the exams is September 11. Note that university portal for students only lists the German name of the lecture, which is "Numerische Methoden für zeitabhängige PDGlen". The exams will be on Friday, September 30. The precise schedule will be available on Monday, September 26.
  • One week before the oral exams, on Wednesday September 21 at 9:45 in room 1.067, we will have our traditional Q&A-session about the lecture. Please prepare questions.
  • The full list of questions for the oral exam can now be found in the Exam section.
  • A complete version of the lecture notes is now available for download.
  • The last problem class on July 20 will be used to answer questions.
  • Update of the lecture notes.
  • Problem sheet 12 is now available.
  • The questions for the exam about Chapters 6 and 7 are now available for download. The questions about the Chapter 8 will follow.
  • The results of the evaluation of the lecture are ready and can be found here .
  • There is an update for the lecture notes.
  • Problem sheet 11 is now available.
  • The lecture notes were updated.
  • Lectures will take place on Wednesday, June 29.
  • Problem sheet 10 is now available.
  • The solution of Problem 30 from sheet 9 is provided under additional material.
  • Problem sheet 9 is now available. To work on the exercise you will further need Gronwall_DixonMcKee.pdf which also can be found here.
  • Small update of the lecture notes at the end of chapter 7.
  • Problem sheet 8 is available.
  • The complete Chapter 7 can now be found in the lecture notes.
  • Lecture notes now contain the complete Section 7.4.
  • Problem sheet 7 is available.
  • Problem sheet 6 is available.
  • Lecture notes update.
  • Problem sheet 5 is available.
  • Problem sheet 4 is available.
  • The lecture notes now contain the complete Section 7.1.
  • The solution to the programming exercise 12 is now available for download.
  • Update of the lecture notes with corrections in Chapter 6 and the first pages of Chapter 7
  • Problem sheet 3 is now available. We strongly suggest to take a look at the programming exercise about Runge-Kutta methods. The files can be found in the category problem sheets.
  • Important announcement:
    The lecture on Tuesdays 9:45 to 11:15 will be in seminar room 2.067 from next week on.
  • Problem sheet 2, which will be discussed next Monday May 2nd, is online.
  • Problem 5 of the first problem sheet is postponed to next week (problem class on 4th May).
  • The first problem sheet is now available. It will be discussed on April 27th.
  • As discussed in the first lecture the problem classes will be on Wednesday.
  • In order to avoid frequent replacements due to obligations of Prof. Hochbruck for the DFG, there is an alternative date for lectures on mondays 15:45 in room 1.067. The lecture dates are always announced here.


  • Prof. Dr. Marlis Hochbruck (lectures)
  • Dipl. math. techn. Simone Buchholz (problem classes)
  • Dipl. math. techn. David Hipp (problem classes)

Weekly hours

4 SWS lecture + 2 SWS problem class

Contents and Prerequisites

The aim of this lecture is to construct, analyze and discuss the efficient implementation of numerical methods for time-dependent partial differential equations (pdes). We will consider traditional methods and techniques as well as very recent research.

The students are expected to be familiar with the basics of the numerical analysis of the time integration of ordinary differential equations (Runge-Kutta and multistep methods) and of finite element methods for elliptic boundary element methods. The lecture starts with a review on Runge-Kutta and multistep methods. Some basic knowledge in functional analysis and the analysis of boundary value problem is helpful but the main results will be repeated in the lecture.



Monday, 15:45-17:15 in SR 1.067, building 20.30 (alternative date)
Tuesday, 9:45-11:15 in SR 2.067, building 20.30
Thursday, 9:45-11:15 in SR 1.067, building 20.30

Problem classes

Wednesday, 9:45-11:15 in SR 3.061, building 20.30

Lecture dates

Please note that the dates for the lectures and problem classes may vary from week to week. The dates for the next weeks are listed below. If changes to already announced dates are required they will be highlighted by color.

cw 16: Tuesday 19.4. and Thursday 21.4.
cw 17: Tuesday 26.4. and Thursday 28.4.
cw 18: Tuesday 03.5. and Wednesday 04.5. (problem classes on Monday 02.5.)
cw 19: Wednesday 11.5. and Thursday 12.5. (problem classes on Tuesday 10.5.)
cw 20: Tuesday 17.5.
cw 21: Monday 23.5. and Tuesday 24.5.
cw 22: Tuesday 31.5. and Thursday 02.6.
cw 23: Tuesday 07.6. and Thursday 09.6.
cw 24: Tuesday 14.6. and Thursday 16.6.
cw 25: Monday 20.6. and Thursday 23.6.
cw 26: Wednesday 29.6. and Thursday 30.6. (problem classes on Tuesday 28.6.)
cw 27: Thursday 07.7.      
cw 28: Monday 11.7. and Thursday 14.7.
cw 29: Monday 18.7. and Tuesday 19.7.


The oral exams will take place on Friday, September 30.

The format of the exams will be the following:

  • Until the end of the semester, we will provide you with a list of possible questions for each chapter of the lecture.
  • You randomly draw three questions from this list, each from another chapter. One question can be redrawn from the same chapter with the possibility to answer the original question.
  • Then you are given 20 minutes for preparation (without any aid). Any notes that you prepare during this time can be used in the oral exam.
  • The actual oral exam will last additional 20 minutes during which you have to answer the questions. This leaves approximatly 7 minutes for each question. If the answer is too short we expect you to present further details of the topic. In order to assure that you understand all aspects of the topic in question, you can always be asked further questions.
  • The final grade will be the mean of the grades (1-6) from the three answered questions.

The list of questions can be found here: Questions

Lecture notes (draft version)

The lecture notes provided here are a draft version, since they are written when the lecture progresses. This includes corrections shortly after the corresponding topic was discussed.

I am gratefull for any suggested corrections and improvements.

The lecture notes are a continuation of the lecture notes for the Finite Element Methods from WS 15/16.

Problem sheets

sheet 1, sheet 2, sheet 3, sheet 4, sheet 5, sheet 6, sheet 7, sheet 8, sheet 9, sheet 10, sheet 11, sheet 12

Additional material:


Further literature will be provided in the lecture