Numerical Analysis and Simulation I: Ordinary Differential Equations (ODEs)

Organizers

Prof. Dr. R. Pulch

Type

Lecture and Exercises (4+2 SWS)

The course comprises 4h lectures and 2h exercises per week.

Target audience

The course is dedicated to students in mathematics, financial mathematics, IT and SII.
Required course for master programme 'Computer Simulation in Science', first term in branch 'Mathematical Modelling'.

Prerequisite

Knowledge of basic courses in mathematics (Analysis I-II, Linear Algebra I-II or similar) and Introduction to Numerical Mathematics (or: block course 'Introduction to Numerical Methods for Computer Simulation').

Credits

9 points

Lab Exercise

Separate course: Lab Exercises for Numerical Analysis and Simulation I: ODEs

Examination

Oral examinations with duration of about 30 min. for each candidate. No books, script, etc. allowed.

Dates:

March, 14

• 9:00-9:30 L.V.
• 9:45-10:15 A.S.
• 10:30-11:00 A.N.
• 11:15-11:45 Ko.S.
• 13:30-14:00 O.L.
• 14:15-14:45 L.B.

April, 18

• 9:00-9:30 Ke.S.
• 9:45-10:15 J.H.
• 10:30-11:00 C.H.
• 11:15-11:45 W.T.
• 13:30-14:00 M.J.

Location:

Campus Wicküler Park (Bendahler Str. 29), room 505 (5th floor)

Topics

ODE models in science; one-step methods; multi-step methods; integration of stiff systems; differential algebraic equations; boundary value problems.

Time and Place

Lecture:
Monday, 10:15-11:45 in room G-15.25
Thursday, 12:15-13:45 in room G-15.25

Office hour

No weekly office hour after February, 3.

Scriptum

Script of the lecture
(last modification on February, 16)

Exercises

• Sheet 1
• Sheet 2
• Sheet 3
• Sheet 4
• Sheet 5
• Sheet 6
• Sheet 7
• Sheet 8
• Sheet 9
• Sheet 10
• Sheet 11
• Sheet 12
• Sheet 13
• Sheet 14
• Sheet 15

A folder with solutions of the exercises can be borrowed for one or two days. The folder is located in the secretary's office at Wicküler Park (Bendahler Str. 29), room 502 (5th floor). Office hours: Monday-Friday from 9:00-11:30.

Literature

• J. Stoer, R. Bulirsch: Introduction to Numerical Analysis. Springer, Berlin, 2002. (Chapter 7)
• J. Stoer, R. Bulirsch: Numerische Mathematik 2. Springer, Berlin, 2005. (Kapitel 7)
• A. Quarteroni, R. Sacco, F. Saleri: Numerical Mathematics. Springer, New York, 2007. (Chapter 11)
• K. Strehmel, R. Weiner: Numerik gewöhnlicher Differentialgleichungen. Teubner, 1995.
• P. Deuflhard, F. Bornemann: Scientific Computing with Ordinary Differential Equations. Springer, New York, 2002.