The group offers various lectures focusing on numerical analysis. Details of lectures offered in the current and previous semesters can be found below on the page.
If you wish to participate in a seminar or reading course, please contact the respective supervisor by email. Dates will then be arranged in consultation with the participants.
If you are interested in a thesis in the field of Numerics and Applied Mathematics, you can contact the secretary or directly contact the group leader Prof. Simeon.
In general, if you have any questions or interest, feel free to contact members of the group or drop by the Felix Klein Center for Mathematics directly.
Contents
Many problems in science, technology, and engineering can be modeled by a set of ordinary differential equations (ODEs). In general, these equations are too complex to be solved analytically. This course provides the necessary tools and methods to treat initial value problems (IVPs) numerically.
The following topics will be covered:
- explicit and implicit one-step methods (Runge-Kutta methods)
- error estimation and step size control
- multistep methods (Adams and BDF methods)
- consistency, stability, and convergence
- methods for stiff problems
Contact time
2 SWS Lecture
1 SWS Tutorial
Prerequisites
Informal:
- "Fundamentals of Mathematics"
- "Introduction to Numerical Methods"
- "Introduction to Ordinary Differential Equations"
Formal:
- None
Frequency
This course is offered every winter term and takes place in the first half of the term.
Links & Contact
Lecturer: Prof. Dr. Bernd Simeon
KIS entries:
Numerical Methods for Ordinary Differential Equations (Lecture)
Numerical Methods for Ordinary Differential Equations (Tutorial)
Course in OLAT:
RPTU Numerical Methods for Ordinary Differential Equations WS 2024/25
Contents
This course introduces the classical theory of partial differential equations (PDEs). In particular, the following topics will be covered:
- classification of PDEs and well-posed problems
- first-order quasi-linear PDEs and Cauchy problems
- second-order linear PDEs: Poisson's equation, heat equation, and wave equation
- separation of variables, fundamental solution, Green's function, maximum principle, and Fourier transform
Contact time
2 SWS Lecture
1 SWS Tutorial
Prerequisites
Informal:
- "Fundamentals of Mathematics"
- "Introduction to Ordinary Differential Equations"
Formal:
- None
Frequency
This course is offered every winter term and takes place in the second half of the term.
Links & Contact
Lecturer: Prof. Dr. Bernd Simeon
KIS entries:
Partial Differential Equations: An Introduction (Lecture)
Partial Differential Equations: An Introduction (Tutorial)
Course in OLAT:
RPTU Partial Differential Equations: An Introduction WS 2024/25
Contents
The theory and numerical analysis of differential-algebraic equations are discussed, in particular:
- fields of application (electrical circuits and multibody mechanical systems)
- relation to singularly perturbed problems
- solution theory and index concepts
- normal form for linear DAEs
- numerical aspects
Contact time
2 SWS Lecture
1 SWS Tutorial
Prerequisites
Informal:
- "Fundamentals of Mathematics"
- "Introduction to Ordinary Differential Equations"
Formal:
- None
Frequency
This course is offered irregularly in winter term.
Links & Contact
Lecturer: Prof. Dr. Bernd Simeon
KIS entries:
Differential-Algebraic Equations (Lecture)
Differential-Algebraic Equations (Tutorial)
Course in OLAT:
RPTU Differential-Algebraic Equations WS 2024/25