TECHNISCHE UNIVERSITÄT BERLIN Regularization of Constrained PDEs of Semi-Explicit Structure

TECHNISCHE UNIVERSITÄT BERLIN Regularization of linear and nonlinear descriptor systems

Differential-algebraic equations (DAEs) present today the state-of-the-art in dynamical systems arising from automated modularized modeling in almost all areas of science and engineering. While the modeling becomes more and more convenient, the resulting models are typically not easy to treat with current numerical simulation, control and optimization methods. In many cases a reformulation of t...

Technische Universität Berlin Institut für Mathematik Regularization and Numerical Simulation of Dynamical Systems Modeled with Modelica

Quasi-linear differential-algebraic equations (DAEs) are essential tools for modeling dynamical processes, e.g. for mechanical systems, electrical circuits or chemical reactions. These models are in general of higher index and contain so called hidden constraints which lead to instabilities and order reductions during numerical integration of the model equations. In this article we consider dyn...

Technische Universität Berlin Institut für Mathematik Fundamental Diagrams and Multiple Pedestrian Streams

Technische Universität Berlin Institut für Mathematik Some Fundamental Considerations for the Application of Macroscopic Models in the Field of Pedestrian Crowd Simulation

TECHNISCHE UNIVERSITÄT BERLIN Efficient integration of matrix-valued non-stiff DAEs by half-explicit methods

Numerical integration methods for nonlinear differential-algebraic equations (DAEs) in strangeness-free form are studied. In particular, half-explicit methods based on popular explicit methods like one-leg methods, linear multi-step methods, and Runge-Kutta methods are proposed and analyzed. Compared with well-known implicit methods for DAEs, these half-explicit methods demonstrate their effici...