Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-80-11A-K-4

Numerics of ODE (2V+1U, 4.5 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U)
2 V Lecture 3.0 CP 28 h 62 h
1 U Exercise class (in small groups) 1.5 CP 14 h 31 h
(2V+1U) 4.5 CP 42 h 93 h

Basedata

SWS 2V+1U
CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. in WiSe
Level [4] Bachelor (Specialization)
Language [EN] English
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-TEMA] Industrial Mathematics
Livecycle-State [NORM] Active

Notice

This course is part of the course [MAT-80-11-K-4] (normally, first half of the semester).

Possible Study achievement

  • Verification of study performance: proof of successful participation in the exercise classes (ungraded)
  • Examination number (Study achievement): 84022 ("Exercise Class Numerical Methods for ODE")
  • Details of the examination (type, duration, criteria) will be announced at the beginning of the course.

Contents

Numeric methods which deal with initial value problems will be discussed. In particular, the following contents are covered:
  • One-step method (explicit/implicit): consistency, convergence, stability,
  • Runge-Kutta methods,
  • Control of step size,
  • Methods for stiff problems: Gauß algorithm, collocation method.

Competencies / intended learning achievements

The students have studied and understand the basic concepts of the numerical treatment of initial value problems as well as the mathematical techniques required to analyze them. They are able to analyze the algorithms and apply them to practical problems. They understand the proofs presented in the lecture and are able to comprehend and explain them.

By completing the given exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. In addition, they have learnt how to apply these techniques to new problems, analyze them and develop solution strategies.

Literature

  • P. Deuflhard, F. Bornemann: Numerische Mathematik II,
  • J. Stoer, R. Bulirsch: Einführung in die Numerische Mathematik II,
  • A. Quarteroni, R. Sacco, F. Saleri: Numerische Mathematik I, II,
  • E. Hairer, G. Wanner: Solving Ordinary Differential Equations I, II,
  • H. Heuser: Ordinary Differential Equations,
  • W. Walter: Ordinary Differential Equations,
  • G. Teschl: Ordinary Differential Equations and Dynamical Systems.

Materials

Further literature will be announced in the lecture; Exercise material is provided.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

References to Course [MAT-80-11A-K-4]

Module Name Context
[MAT-30-10L-M-5] Specialisation Module (Teachers Training Programme Mathematics) WP: Obligation to choose in Obligatory-Modulteil #A (Lectures) 2V, 3.0 LP
[MAT-80-11A-M-4] Numerics of ODE P: Obligatory 2V+1U, 4.5 LP
[MAT-80-11-M-4] Differential Equations: Numerics of ODE & Introduction to PDE P: Obligatory 2V+1U, 4.5 LP
Course-Pool Name
[MAT-70-2V-KPOOL-4] Elective Courses Analysis and Stochastics (2V, B.Sc.)
[MAT-80-2V-KPOOL-4] Elective Courses Modelling and Scientific Computing (2V, B.Sc.)