Differential-Algebraic Systems Group


Courses in Winter Term 2021/22

Our group offers the following courses in winter term 2021/22:

 

Numerical Methods for Ordinary Differential Equations

Differential-Algebraic Equations

Proseminar "B-Splines and NURBS"

Numerical Methods for Ordinary Differential Equations

Contents

Most problems in science, technology, and engineering can be modeled by a set of differential equations. In general, these equations are too complex to be solved analytically. This course provides the necessary tools and methods to treat initial value problems 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

Differential-Algebraic Equations

Contents

The theory and numerical analysis of differential-algebraic equations are discussed, in particular:

  • application fields (electrical circuits and multibody mechanical systems)
  • relation with 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.

Proseminar "B-Splines and NURBS"

Contents

A presentation of the proseminar can be found at the following link.

Contact time

2 SWS Seminar

Prerequisites

Informal:

  • "Fundamentals of Mathematics"
  • Basic programming knowledge

Formal:

  • None

Courses in Summer Term 2021

Our group offers the following courses in summer term 2021:

 

Numerical Methods for Partial Differential Equations I

Scientific Computing in Solid Mechanics

Numerical Methods for Partial Differential Equations I

Contents

To describe real-world processes, one often makes use of partial differential equations, which, in general, cannot be solved analytically. In this course, we will discuss and study the mathematical techniques required for solving such equations numerically. The focus lies on the discretization of boundary value problems for elliptic differential equations with finite difference or finite element methods. At the end of the course, these ideas will be applied to parabolic differential equations.

The following topics will be covered:

  • approximation methods for elliptic problems
  • theory of weak solutions
  • consistency, stability, and convergence
  • approximation methods for parabolic problems

Contact time

4 SWS Lecture
2 SWS Tutorial

Prerequisites

Informal:

  • "Fundamentals of Mathematics"
  • "Numerics of ODE"
  • "Introduction to PDE"
  • Some functional analysis

Formal:

  • None

Scientific Computing in Solid Mechanics

Contents

Mathematical modelling, numerical methods, and software for the following topics:

  • elastic bodies
  • special cases of beams and plane strain/stress state
  • finite element space discretisation
  • specific time integration schemes

Contact time

2 SWS Lecture

Prerequisites

Informal:

  • "Fundamentals of Mathematics"
  • "Introduction to Numerical Methods"
  • "Numerics of ODE"
  • "Introduction to PDE"

Formal:

  • None

Frequency

This course is offered irregularly.

Zum Seitenanfang