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

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

23.06.2019 Chapter 7: Finite difference methods: Stability and convergence pdf (Chapter 7)
18.06.2019 Chapter 7: Boundary value problems; finite difference methods; idea and consistency
18.06.2019 Chapter 6: Symmetric integrators have even consistency order, splitting methods (Lie-Trotter vs. Strang) pdf (Chapter 6)
13.06.2019 Exercise Sheet 11 (added information for exercise 3 on 18.06.2019) pdf
06.06.2019 Exercise Sheet 10 pdf
04.06.2019 Chapter 6: Partitioned RK methods (symplectic Euler, Störmer-Verlet), symmetric integrators, Gauss collocation is symmetric
03.06.2019 Chapter 6: Symplectic integrators, explicit and implicit Euler are not symplectic, symplectic Runge-Kutta methods
29.05.2019 Exercise Sheet 9 (typo corrected on 31.05.2019) pdf
28.05.2019 Chapter 6: Symplecticity, symplectic group, Poincare's characterization of Hamiltonian systems
27.05.2019 Chapter 6: Geometric integrators: Hamiltonian systems, examples, invariants
21.05.2019 Chapter 5: A-stability, A(alpha)-stability, consequences of second Dahlquist barrier pdf (Chapter 5)
20.05.2019 Chapter 5: convergence implies consistency; consequences of first Dahlquist barrier
17.05.2019 Exercise Sheet 8 pdf
14.05.2019 Chapter 5: Examples; convergence implies root condition; consistency of linear multi-step methods
13.05.2019 Chapter 5: lemmas for convergence theorem; Adams-Bashforth method
09.05.2019 Exercise Sheet 7 pdf
08.05.2019 Chapter 5: Multi-step methods; consistency and convergence
07.05.2019 Chapter 4: B-stability, AN-stability, BN-stability; Chapter 5: Multi-step methods pdf (Chapter 4)
30.04.2019 Exercise Sheet 6 pdf
30.04.2019 Chapter 4: Stability domains, A-stability, L-stability, Radau-IIA methods
29.04.2019 Chapter 4: Stiff ODEs: Introduction, example, stability function of RK methods
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

 05.05.2019 Lecture notes: Chapter 2-3 (complete), Chapter 4 (parts) pdf 12.04.2019 Lecture notes: Chapter 2 and 3 (complete) 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:

• Monday 09:00 - 10:30, seminar room SEM DA grün 04 (green section, 4. floor)
• Tuesday 09:00 - 10:30, seminar room SEM DA grün 04 (green section, 4. floor)
The lecture is accompanied by an exercise class (either in German or in English).
• English: Wednesday 15:00 - 16:30 (taught by Markus Tempelmayr), seminar room SEM DA 06B (green section, 6. floor)
• German: Friday 09:00 - 10:30 (taught by Michael Innerberger), seminar room SEM DA 03A (green section, 3. floor)
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.