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20051103BuchLinear index1 DAEs: regular and singular problems Riaza, Ricardo; März, RoswithaSeveral features and interrelations of projector methods and reduction techniques for the analysis of linear timevarying differentialalgebraic equations (DAEs) are addressed in this work. The application of both methodologies ...

20051102BuchManaging the driftoff in numerical index2 differential algebraic equations by projected defect corrections März, RoswithaWhen integrating index2 differentialalgebraic equations, the given constraint may be failed to be met due to the integration method itself and also due to numerical defects in the realization. This socalled driftoff ...

20051104BuchNonlinear differentialalgebraic equations with properly formulated leading term März, RoswithaNonlinear differentialalgebraic equations with properly stated leading term of index one and two are characterized. Linearization and the solvability of perturbed problems are considered.

20051020BuchNumerical stability criteria for differentialalgebraic systems März, RoswithaIn this paper we transfer classical results concerning Lyapunov stability of stationary solutions x* to the classes of DAEs being most interesting for circuit simulation, thereby keeping smoothness as low as possible. We ...

20051104BuchNumerically well formulated index1 DAEs Higueras, Inmaculada; März, Roswitha; Tischendorf, CarenFor index1 DAEs with properly stated leading term, we characterize dissipative and contractive flows and study how the qualitative properties of the DAE solutions are reflected by numerical approximations. The best situation ...

20051104BuchNumerically well formulated index2 DAEs Higueras, Inmaculada; März, Roswitha; Tischendorf, CarenFor linear index2 DAEs with properly stated leading term we characterize contractive and dissipative flows. We study under which conditions the qualitative properties of the DAE solutions are reflected by the numerical ...

20051116BuchOn asymptotics in case of linear index2 differentialalgebraic equations Hanke, Michael; Macana, Ebroul Izquierdo; März, RoswithaAsymptotic properties of solutions of general linear differentialalgebraic equations (DAE's) and those of their numerical counterparts are discussed. New results on the asymptotic stability in the sense of Lyapunov as ...

20051021BuchOn linear differentialalgebraic equations and linearizations März, RoswithaOn the background of a careful analysis of linear DAEs, linearizations of nonlinear index2 systems are considered. Finding appropriate function spaces and their topologies allows to apply the standard Implicit Function ...

20051103BuchOn linear differentialalgebraic equations with properly stated leading term März, Roswitha; Riaza, RicardoWe consider in this work linear, timevarying differentialalgebraic equations (DAEs) of the form A(t)(D(t)x(t))'+B(t)x(t)=q(t) through a projector approach. Our analysis applies in particular to linear DAEs in standard ...

20051103BuchOn linear differentialalgebraic equations with properly stated leading term März, Roswitha; Riaza, RicardoThis paper addresses critical points of linear differentialalgebraic equations (DAEs) of the form A(t)(D(t)x(t))' + B(t)x(t) = q(t) within a projectorbased framework. We present a taxonomy of critical points which reflects ...

20051107BuchOn linearquadratic optimal control problems for timevarying descriptor systems Kurina, Galina A.; März, RoswithaThe solvability of a linearquadratic optimal control problem in a Hilbert space for timevarying descriptor systems is established under some conditions. Unlike previous works of other authors that are devoted to ...

20051104BuchPDAEs and Further Mixed Systems as Abstract Differential Algebraic Systems Lamour, René; März, Roswitha; Tischendorf, CarenAbstract differential algebraic systems (ADASs), i.e., differential algebraic systems with operators acting in real Hilbert spaces are introduced for a systematical treatment of coupled systems of PDEs, DAEs and integral ...

19920101BuchPreface Griepentrog, Eberhard; Hanke, Michael; März, Roswitha

20051103BuchProjectors for matrix pencils März, RoswithaIn this paper, basic properties of projector sequences for matrix pairs which can be used for analyzing differential algebraic systems are collected.

20051021BuchRecent results in solving index 2 differentialalgebraic equations in circuit simulation März, Roswitha; Tischendorf, CarenIn electric circuit simulation the charge oriented modified nodal analysis may lead to highly nonlinear DAEs with low smoothness properties. They may have index 2 but they do not belong to the class of Hessenberg form ...

20051104BuchSingularities of linear timevarying DAEs Riaza, Ricardo; März, RoswithaSingular issues arising in linear timevarying differentialalgebraic equations are addressed in this paper. We review the use of projector methods based upon the tractability index concept for the analysis of regular ...

20051104BuchSolvability of linear differential algebraic equations with properly stated leading terms März, RoswithaIn this paper, general solvability statements on linear continuous coefficient differential algebraic equations with properly stated leading terms are derived by means of decoupling projector functions decomposing the ...

20051115BuchStability of periodic solutions of index2 differential algebraic systems Lamour, René; März, Roswitha; Winkler, RenateThis paper deals with periodic index2 differential algebraic equations and the question whether a periodic solution is stable in the sense of Lyapunov. As the main result, a stability criterion is proved.This criterion ...

20051104BuchThe index of linear differential algebraic equations with properly stated leading terms März, RoswithaIn a linear differential algebraic equation with properly stated leading term, the involved derivatives of the unknown function are figured out by an additional matrix coefficient being in some sense well matched with the ...

19920101BuchToward a better understanding of differential algebraic equations (Introductory survey) Griepentrog, Eberhard; Hanke, Michael; März, Roswitha