101.316 VO, 106.065 UE (4std Vorlesung + 2std Übung, Sommersemester 2019)
Numerics of differential equations
TISS-Homepage (101.316)
TISS-Homepage (106.065)

As agreed with the participants, the lecture will be held in English!

Downloads

datetopiclink
11.04.2019 Exercise Sheet 5 pdf
09.04.2019 Chapter 3: Collocation vs. quadrature pdf (Chapter 3)
08.04.2019 Chapter 3: Convergence of collocation schemes  
03.04.2019 Exercise Sheet 4 pdf
02.04.2019 Chapter 3: Collocation methods; well-posedness; consistency order  
01.04.2019 Chapter 3: RK methods and quadrature; consistency conditions; Langrange interpolation  
27.03.2019 Exercise Sheet 3 (hint to ex. 2 added on 29.03.2019) pdf
26.03.2019 Chapter 3: Implicit one-step methods; fundamentals; implicit Runge-Kutta methods  
25.03.2019 Chapter 2: Adaptive algorithm; idea of time-step control (h-h/2 error estimation strategy) pdf (Chapter 2)
20.03.2019 Exercise Sheet 2 (three typos corrected on 25.03.2019) pdf
19.03.2019 Chapter 2: Remarks on consistency of RK methods; idea of time-step control (one-step methods of different orders)  
18.03.2019 Chapter 2: Explicit Runge-Kutta methods; stability; consistency conditions  
13.03.2019 Exercise Sheet 1 pdf
12.03.2019 Chapter 2: Convergence; 2nd order methods: modified Euler method; Heun method  
11.03.2019 Chapter 2: Explicit one-step methods; consistency; explicit Euler method  
11.03.2019 Chapter 1: Continuous dependence on the data pdf (Chapter 1)
05.03.2019 Chapter 1: Basic about ODEs: Peano theorem; Picard-Lindelöf theorem; Gronwall lemma  

Lecture notes

12.04.2019 Lecture notes: Chapter 2 and 3 (complete) pdf
12.04.2019 Lecture notes: Chapter 3 (complete)  
08.04.2019 Lecture notes: Chapter 3 (first parts only)  

Schedule

The lecture starts on Tuesday March 05, 2019. The lecture times are:

The lecture is accompanied by an exercise class (either in German or in English). The exercise class starts on Wednesday March 20 and Friday March 22, respectively. Please register at TISS for one of the exercise classes. The English exercise class is (essentially) restricted to students of the MSc studies Mathematical Modelling in Engineering.

Subject of the course

Initial- and boundary value problems for ordinary and partial differential equations: One-step and multi-step methods, adaptivity. Introduction to numerical methods for partial differential equations of elliptic, parabolic, and hyperbolic type.

Examination modalities

Assesment of the exercise class is based on the number of prepared exercises and presentation thereof. Attendance in the exercise class is mandatory. You can be absent once due to legitimate reasons (sickness, etc.). In this case, please notify your tutor in advance:

Examination of the lecture is oral. To make an appointment, please write an email to dirk.praetorius@asc.tuwien.ac.at. Please do this around one week ahead of your desired examination day.