AbstractsMathematics

In recent years, the use of differential equations in connection with algebraic constraints on the variables has become a widely accepted tool for modeling the dynamical behaviour of physical processes. Compared to ordinary differential equations (ODEs), it has been observed that a number of difficulties can arise when numerical methods are used to solve differential-algebraic equations (DAEs), for instance order reduction phenomena, drift-off effects or instabilities. DAEs arise naturally and have to be solved in a variety of applications such as the mathematical pendulum and a reheat furnace model, both of which are used in this thesis to demonstrate the application of numerical methods and the arising difficulties. Working towards the prospective development of an applicable NMPC algorithm with DAEs as system models, this thesis is mainly concerned with the analysis and numerical treatment of DAEs. A particular focus is put on the topics of the strangeness index, an iterative procedure for determining all hidden constraints, regularisation techniques and numerical methods for solving DAEs. This includes the implementation of the RadauIIa and BDF methods. Due to a multitude of examples, this thesis may serve as an accessible introduction to DAEs and as a foundation for future research into this field.