Description: Extending basic knowledge on odes from Numerik I, we first concentrate on one-step methods for stiff and differential-algebraic systems and then discuss Hamiltonian systems. In the second part of the lecture we consider the iterative solution of large linear systems.

Literature: 

Lecture Notes on Numerical Methods for ODEs and Numerical Linear Algebra (NumericsII), Ralf Kornhuber, FU Berlin

Lecture Notes: Numerical Solution of Ordinary Differential Equations, Endre Süli, University of Oxford, 2022

Quarteroni, Alfio, Riccardo Sacco, and Fausto Saleri. Numerical mathematics. Vol. 37. Springer Science & Business Media, 2006.

Deuflhard, Peter und Folkmar Bornemann: Scientific computing with ordinary differential equations. Springer, Berlin, 2002.

Tutorial

• Each week a sheet with exercises will be made available electronically on the white board
• The exercises are intended to be solved by teams of two members.
• The exercises consist of theoretical and numerical problems. The latter should be solved using Python or Matlab. Both types of exercises are rated seperately
• Active participation: at least 50% of both parts (theoretical and programming) and presenting at least one of the problems during the tutorial 
• The grade of this course is based only on the result of the exam.

Target Audience: Students of Bachelor and Master courses in Mathematics and of BMS

Prerequisites: Basics of calculus (Analysis I, II) linear algebra (Lineare Algebra I, II) and numerical analysis (Numerik I)