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We present a qualitative eigenvalue analysis of differential algebraic equations with a certain structure. The structure refers to hybrid modells of linear dynamic networks. In particular, we present a characterization for the existence of purely imaginary eigenvalues. This qualitative question becomes important in applications as electric or water tube networks when studying undamped oscillations. [ABSTRACT FROM AUTHOR]

The simulation of complex systems describing different physical effects becomes more and more of interest in various applications. Examples are couplings describing interactions between circuits and semiconductor devices, circuits and electromagnetic fields, fluids and structures. The modeling of such complex processes [1, 2, 3, 4, 7, 8] often leads to coupled systems that are composed of ordinary differential equations (ODEs), differential-algebraic equations (DAEs) and partial differential equations (PDEs). Such coupled systems can be regarded in the general framework of abstract differential-algebraic equations. Here, we discuss a Galerkin approach for handling linear abstract differential-algebraic equations with monotone operators. It is shown to provide solutions that converge to the unique solution of the abstract differential-algebraic system. Furthermore, the solution is proved to depend continuously on the data. The most interesting point of the Galerkin approach is the choice of basis functions. They have to be chosen in proper subspaces in order to guarantee that the solution satisfies the non-dynamic constraints. In contrast to other approaches as e.g. [5, 6], this approach allows time dependent operators but needs monotonicity. [ABSTRACT FROM AUTHOR]

We study the structure of electrical circuits including a new kind of circuit element named memristors modeled by a differential-algebraic equation (DAE). In 2008 a physical model of the memristor was announced [1] and has attract a great attention. The goal is to characterize the tractability index under strict passivity assumptions. We extend the topological index criteria for the modified nodal analysis (MNA) to that enlarged model including memristors and present an algorithm for the calculation of a consistent initialization for the system. [ABSTRACT FROM AUTHOR]

We study a coupled system coming from circuit simulation with semiconductors. The circuit itself is modeled by the modified nodal analysis and the stationary drift diffusion model is used for the semiconductors. The space discretization is done with finite elements and the Scharfetter-Gummel discretization. The resulting system can be analyzed as a differential algebraic equation with properly stated leading term. Furthermore we give topological index one criteria. Time discretization is done with the standard BDF methods and we obtain a convergence estimate for the whole coupled system close to equilibrium. [ABSTRACT FROM AUTHOR]

Circuit simulation as well as multibody system simulation have been widely used during the last decades. Automatically generated models are known to lead to differential-algebraic equations (DAEs) with higher index in both cases. Whereas multibody system models lead to DAEs of index 3, circuit models have usually index 2. Nevertheless, there is a close connection between oth models. We show here, that a simple change in the circuit modelling process leads to DAEs of index 3 with the same structure as multibody system models have. Furthermore, we present a change in the modelling process of multibody systems that provides DAEs of index 2, similar to the systems known from circuit modeling. An extension of this index reduction process allows even an index-1 DAE description for circuit systems as well as for multibody systems. The most interesting point is here that these modeling steps avoid computations of additional (hidden) constraints. Furthermore, the original contraints are kept, hence the index reduced modell does not suffer from drift effects. [ABSTRACT FROM AUTHOR]

The article offers information on the symposium which will discuss differential algebraic equations (DAEs), partial differential algebraic equations (PDAEs) and their applications.