Universität Wien

250002 VU Numerische Methoden für Differentialgleichungen (2021S)

7.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Continuous assessment of course work
Moodle

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

max. 25 participants
Language: German

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 01.03. 16:45 - 18:15 Digital
  • Wednesday 03.03. 16:45 - 18:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 08.03. 16:45 - 18:15 Digital
  • Wednesday 10.03. 16:45 - 18:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 15.03. 16:45 - 18:15 Digital
  • Wednesday 17.03. 16:45 - 18:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 22.03. 16:45 - 18:15 Digital
  • Wednesday 24.03. 16:45 - 18:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 12.04. 16:45 - 18:15 Digital
  • Wednesday 14.04. 16:45 - 18:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 19.04. 16:45 - 18:15 Digital
  • Wednesday 21.04. 16:45 - 18:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 26.04. 16:45 - 18:15 Digital
  • Wednesday 28.04. 16:45 - 18:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 03.05. 16:45 - 18:15 Digital
  • Wednesday 05.05. 16:45 - 18:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 10.05. 16:45 - 18:15 Digital
  • Wednesday 12.05. 16:45 - 18:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 17.05. 16:45 - 18:15 Digital
  • Wednesday 19.05. 16:45 - 18:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 26.05. 16:45 - 18:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 31.05. 16:45 - 18:15 Digital
  • Wednesday 02.06. 16:45 - 18:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 07.06. 16:45 - 18:15 Digital
  • Wednesday 09.06. 16:45 - 18:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 14.06. 16:45 - 18:15 Digital
  • Wednesday 16.06. 16:45 - 18:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 21.06. 16:45 - 18:15 Digital
  • Wednesday 23.06. 16:45 - 18:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 28.06. 16:45 - 18:15 Digital
  • Wednesday 30.06. 16:45 - 18:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

Introduction to Differential Equations (DE) in 1-d (with material from Analysis I): Cauchy problem, Peano Theorem, Boundary value problems, ...
Basic concepts of numerics: machine arithmetics, condition, error propagation, ...
Basic notions of numerics for DE: stability, consistency, convergence, ...
Basic numerical methods for ordinary and partial DE:
Euler method explicit / implicit, Runge-Kutta, Multistep, Predictor-Corrector, Notions of solutions for DE (strong / weak solutions), Introduction to Partial differential equations, Finite Element Methods, Finite difference methods,
Spectral methods and basics of Fourier expansions,
„Numerical modeling“ with Differential equations.

In the final weeks of the VU, a project example will be worked out and presented in small groups.

Assessment and permitted materials

Grades will be based on an exam at the end of the semester, the number and quality of presented exercise problems, and the project, as well as participation during the course.

Minimum requirements and assessment criteria

This course conveys, by means of a lecture, exercise problems and a small project: basic knowledge on Differential equations, numerical methods for their solutions and elementary numerical analysis of such methods, numerical modeling.

Examination topics

The main part of this course will be given as a lecture. Additionally, exercise problems and projects will be presented by the students at some of the dates.

Reading list

lecture notes tailored for the course.

additional reading (far beyond the contence of the course):

Quarteroni, Sacco, Salieri: Numerical Mathematics, Springer, 2000 (Kap. 2, 11, 12).
Stoer, Bulirsch, Numerische Mathematik 2, Springer-Verl. 2005.
Rannacher, Rolf: Numerik 1: Numerik gewöhnlicher Differentialgleichungen, Heidelberg University Publishing, 2017 https://doi.org/10.17885/heiup.258.342.
Peter Deuflhard, Folkmar Bornemann, Numerische Mathematik 2: Gewöhnliche Differentialgleichungen, De Gruyter, 2008.

Association in the course directory

WND

Last modified: Fr 12.05.2023 00:21