# Numerics II

## News

- The
**results of the second exam**can be found here. - For your preparation for the second exam, the exercise sheet of the first exam is avaliable here.
- You can have a look at the exact grading of your exam on Fri, 2016-04-08, from 13:00 to 14:00. The exact place for this will be announced here. It will be either room 121, 126, or 131 in Arnimallee 6.
- The
**results of the first exam**can be found here. There will be the possibility to have a look at the exact grading of your exam and possible remarks. Details will be announced here soon. - Example matlab programs for exercise 4 are now online (see below).
- The office hour on Tuesday, 2015-12-15, is shifted to 13:00-14:00.
- The office hour on Tuesday, 2015-11-24, is shifted to 13:00-14:00, the one on Tuesday, 2015-12-01, is canceled.
- The office hour on Tuesday, 2015-10-27, is canceled.

## Dates

Lecture | Fri, 12:15 - 13:45 | Arnimallee 6, SR 031 |

Fri, 14:15 - 15:45 | Arnimallee 6, SR 031 | |

Tutorial | Thu, 12:15 - 13:45 | Arnimallee 6, SR 009 |

Exam | Fri, 2016-02-12, 12-14 | Arnimallee 6, SR 031 |

Second exam | Fri, 2016-04-15, 12-14 | Arnimallee 6, SR 031 |

## General Information

### 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.

### 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)

## Registration

All participants should register at the KVV, so that we know who is participating. The overall number of participants is also necessary to justify the equipment of the course. In addition, depending on your program of study, you have to register in the Campus Management.

## Exercises and Criteria for a Certificate

### Tutorial & Exercises

- The tutorial offers the possibility to discuss and better understand the presented material and exercises. Furthermore solutions of exercises are presented by the students.
- Each week a sheet with exercises will be made available electronically on this web page (see below).
- The exercises are intended to be solved by teams of three members.
- The exercises consist of theoretical and numerical problems. The latter should be solved using Matlab (available at the students computer pool at the institute). Both types of exercises are rated seperately.
- The solutions have to be finished before the tutorial two weeks after they were handed out.
- The solutions of the numerical problems should be delivered by email to graeser@math.fu-berlin.de. Note that a complete solution for a numerical experiment consists of a running Matlab code, a program executing the required test runs, and protocols of the execution of these test runs. Delivering a correct and running code without knowing what is going on in the code will be regarded and rated as attempt of deception.
- The solutions of the theoretical problems have to be presented in the tutorial on request (without regard to preference and presence) by a member of a given group.

### Exercises

Example programs for exercises can be found here.

- Exercise 1 (updated, add possible scoring of exercise) (explicit Runge-Kutta example).
- Exercise 2
- Exercise 3
- Exercise 4 (implicit linear Runge-Kutta example).
- Exercise 5
- Exercise 6
- Exercise 7
- Exercise 8
- Exercise 9

## Accompanying Material

### Lecture Notes

The lecture notes are available here.

### Matlab

Here you can find an introduction to Matlab (in german, sorry).

## Literature

The following selection of textbooks can be found in the library.

- Deuflhard, Peter: Newton Methods for Nonlinear Problems. Springer, Berlin, 2004.
- Deuflhard, Peter und Folkmar Bornemann: Numerische Mathematik II - Gewöhnliche Differentialgleichungen. Walter de Gruyter, Berlin, 2002.
- Deuflhard, Peter und Folkmar Bornemann: Scientific computing with ordinary differential equations. Springer, Berlin, 2002.
- Deuflhard, Peter und Andreas Hohmann: Numerische Mathematik I - Eine algorithmisch orientierte Einführung. Walter de Gruyter, Berlin, 2002.
- Golub, Gene und Charles Van Loan: Matrix computations. Johns-Hopkins-University Press, Baltimore, 1993.
- Hairer, Ernst, Syvert Paul Nørsett und Gerhard Wanner: Solving Ordinary Differential Equations I - Nonstiff Problems, Band 8 der Reihe Springer Series in Computational Mathematics. Springer, Berlin, Heidelberg, New York, 1987.
- Hairer, Ernst und Gerhard Wanner: Solving Ordinary Differential Equations II - Stiff and Differential-Algebraic Problems, Band 14 der Reihe Springer Series in Computational Mathematics. Springer, Berlin, Heidelberg, New York, 1991.
- Meister, Andreas: Numerik linearer Gleichungssysteme. Vieweg, Braunschweig, 1999.
- Ortega, James und Werner Rheinboldt: Iterative solution of nonlinear equations in several variables. Academic Press, New York, 1972.
- Quarteroni, Alfio, Riccardo Sacco und Fausto Saleri: Numerische Mathematik 1. Springer, Berlin, 2002.
- Quarteroni, Alfio, Riccardo Sacco und Fausto Saleri: Numerische Mathematik 2. Springer, Berlin, 2002.
- Stoer, Josef und Roland Bulirsch: Numerische Mathematik - eine Einführung, Band 1. Springer, Berlin, 2005. aus dem FU-Netz auch Online verfügbar: http://www.springerlink.com/content/q1x448/fulltext.pdf.
- Stoer, Josef und Roland Bulirsch: Numerische Mathematik - eine Einführung, Band 2. Springer, Berlin, 2005. aus dem FU-Netz auch Online verfügbar: http://www.springerlink.com/content/v76507/fulltext.pdf.
- Walter, Wolfgang: Gewöhnliche Differentialgleichungen - eine Einführung. Springer, Berlin, 1996.
- Werner, Dirk: Funktionalanalysis. Springer, Berlin, 2000.

Further literature on numerics is deposited under the shelf marks H.1.0 and H.1.1.

Introductory literature in computer science can be found under XA.1, introductions in Unix operating system under XD.4.0.

## Contact

Prof. Dr. Carsten Gräser | graeser@mi.fu-berlin.de | Arnimallee 6, Raum 121 Sprechstunde: Di 14:00-15:00 |