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Known solvability results for nonlinear index-1 differential-algebraic equations (DAEs) are in general local and rely on the Implicit Function Theorem. In this paper, we derive a global result which guarantees unique solvability on a given time interval for a certain class of index-1 DAEs with certain monotonicity conditions. Based on this result, we show that memristive circuit DAEs arising from the modified nodal analysis are uniquely solvable if they fulfill certain passivity and network topological conditions. Furthermore we present an error estimation for the solution with respect to perturbations on the right-hand side and in the initial value. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY The hyperbolicity problem in circuit theory concerns the existence of purely imaginary eigenvalues in the linearization of the time-domain description of the circuit dynamics. In this paper, we characterize the circuit configurations that, in a strictly passive setting, yield purely imaginary eigenvalues for all values of the capacitances and inductances. Our framework is based on branch-oriented, semistate (differential-algebraic) circuit models that capture explicitly the circuit topology, and use several notions and results from digraph theory. So-called P-structures arising in the analysis turn out to be the key element supporting our results. The analysis is shown to hold not only for classical (RLC) circuits but also for nonlinear circuits including memristors and other mem-devices. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: One challenge for the simulation and optimization of real gas pipe networks is the treatment of compressors. Their behavior is usually described by characteristic diagrams reflecting the connection of the volumetric flow and the enthalpy change or shaft torque. Such models are commonly used for an optimal control of compressors and compressor stations [4,7] using stationary models for the gas flow through the pipes. For transient simulations of gas networks, simplified compressor models have been studied in [1–3]. Here, we present a transient simulation of gas pipe networks with characteristic diagram models of compressors using a stable network formulation as (partial) differential‐algebraic system. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

We consider partial differential algebraic systems (PDAEs) describing water transportation networks. Similar to the approach in [6], we follow the method of lines for the discretization. However, we do not consider free surface flow models but pressure flow models covering hydraulic shocks. Moreover, we include switching models reflecting the on/off state of pumpes and valves. Aiming at a stable numerical simulation of the PDAEs we present a topology based spatial discretization that results in a differential algebraic system (DAE) of index 1. Furthermore we show that the DAE index can be higher than 1 if the spatial discretization is not adapted to the position of reservoirs and demand nodes within the network. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]