Geometric Numerical Integration 1

What it is about

You learn the fundamentals of geometric (structure-preserving) numerical integration for ordinary differential equations. In the end you can recognize different geometric structures in differential equations and select and apply suitable numerical methods that preserve these structures.

What you will be able to do

• Identify geometric structures in ODEs
• Overview of modern structure-preserving integrators
• Choose suitable methods for given preservation properties
• Implementation of appropriate integrators
• Demonstrate preservation properties by direct computation, discrete Noether theorem, or backward error analysis

What the module consists of

• VorlesungDelivery of content through lectures, examples and discussion; motivation for independent engagement
• ÜbungenProblem sheets with solutions for self-check and deepening of lecture content

Teaching method

• Vortrag mit TafelarbeitExplanation of concepts through examples and discussion; impetus for independent literature work
• Übungsaufgaben mit MusterlösungenIndependent control and deepening of the learned methods