Numerics II

News

Dates

Lecture Mon, 10:15 - 13:45 Arnimallee 6, SR 025/26
Wed, 12:15 - 13:45 Arnimallee 3, SR 130
Tutorial Wed, 14 - 16 Arnimallee 14, 1.3.48 SR T3
Exam Mon, 2018-02-12, 10-12 Arnimallee 6, SR 031
Second exam Tue, 2018-04-10, 10-12 Arnimallee 6, SR 025/26

General Information

Description

Extending basic knowledge on odes from Numerics 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

Exercises

Example programs for exercises can be found here.

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.

  1. Deuflhard, Peter: Newton Methods for Nonlinear Problems. Springer, Berlin, 2004.
  2. Deuflhard, Peter und Folkmar Bornemann: Numerische Mathematik II - Gewöhnliche Differentialgleichungen. Walter de Gruyter, Berlin, 2002.
  3. Deuflhard, Peter und Folkmar Bornemann: Scientific computing with ordinary differential equations. Springer, Berlin, 2002.
  4. Deuflhard, Peter und Andreas Hohmann: Numerische Mathematik I - Eine algorithmisch orientierte Einführung. Walter de Gruyter, Berlin, 2002.
  5. Golub, Gene und Charles Van Loan: Matrix computations. Johns-Hopkins-University Press, Baltimore, 1993.
  6. 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.
  7. 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.
  8. Meister, Andreas: Numerik linearer Gleichungssysteme. Vieweg, Braunschweig, 1999.
  9. Ortega, James und Werner Rheinboldt: Iterative solution of nonlinear equations in several variables. Academic Press, New York, 1972.
  10. Quarteroni, Alfio, Riccardo Sacco und Fausto Saleri: Numerische Mathematik 1. Springer, Berlin, 2002.
  11. Quarteroni, Alfio, Riccardo Sacco und Fausto Saleri: Numerische Mathematik 2. Springer, Berlin, 2002.
  12. 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.
  13. 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.
  14. Walter, Wolfgang: Gewöhnliche Differentialgleichungen - eine Einführung. Springer, Berlin, 1996.
  15. 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
Ana Djurdjevac (Assistentin) adjurdjevac@math.fu-berlin.de Arnimallee 6, Raum 120
Sprechstunde: nach Vereinbarung