Browsing Preprints aus dem Institut für Mathematik by Title
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20051102BuchFeedback solutions of optimal control problems with DAE constraints An optimal feedback control has been obtained for linearquadratic optimal control problems with constraints described by differentialalgebraic equations. For that purpose, a new implicit Riccati equation (Riccati ...

20051107BuchFinding Beneficial DAE Structures in Circuit Simulation Circuit simulation is a standard task for the computeraided design of electronic circuits. The transient analysis is well understood and realized in powerful simulation packages for conventional circuits. But further ...

20051102BuchFine decouplings of regular differential algebraic equations In this paper, the previously formulated conjecture concerning the existence of fine and complete decouplings of regular DAEs with tractability index $\mu$ is verified.

20051107BuchFormulating differential algebraic equations properly

20050408BuchFramework For The A Posteriori Error Analysis Of Nonconforming Finite Elements This paper establishes a unified framework for the a posteriori error analysis of a large class of nonconforming finite element methods. The theory assures reliability and efficiency of explicit residual error estimates ...

20110927BuchFrom convergence principles to stability and optimality We show in a rather general setting that Hoelder and Lipschitz stability properties of solutions to variational problems can be characterized by convergence of more or less abstract iteration schemes. Depending on the ...

20051103BuchGeneral linear methods for linear DAEs For linear differentialalgebraic equations (DAEs) with properly stated leading terms the property of being numerically qualified guarantees that qualitative properties of DAE solutions are reflected by the numerical ...

20051103BuchGeneral Linear Methods for nonlinear DAEs in Circuit Simulation The Modified Nodal Analysis leads to differential algebraic equations with properly stated leading terms. In this article a special structure of the DAEs modelling electrical circuits is exploited in order to derive a new ...

20080307BuchGeometric Brownian Motion with delay mean square characterisationA geometric Brownian motion with delay is the solution of a stochastic differential equation where the drift and diffusion coefficient depend linearly on the past of the solution, i.e. a linear stochastic functional ...

20051111BuchGlobal convergence of multidirectional algorithms for unconstrained optimization in normed spaces Global convergence theorems for a class of descent methods for unconstrained optimization problems in normed spaces, using multidirectional search, are proved. Exact and inexact search are considered and the results allow ...

20051117BuchGlobal Weak Solutions and Uniqueness for a Moving Boundary Problem for a Coupled System of Quasilinear DiffusionReaction Equations arising as a Model of Chemical Corrosion of Concrete Surfaces (Part 3)We show existence and uniqueness for global weak solutions of a moving boundary problem for a coupled system of three quasilinear diffusionreaction equations. The model is briefly described. The proofs are based on ...

20051117BuchGlobal Weak Solutions and WellPosedness of Weak Solutions for a Moving Boundary Problem for a Coupled System of DiffusionReaction Equations arising in the Corrosion Modeling of Concrete (Part 2)The evolution of the corrosion interface separating the uncorroded concrete part and the corroded part of a partially wet concrete wall of a pipe under the influence of hydrogen sulfide can be modelled by a moving boundary ...

19980110BuchHeights on elliptic curves and the diophantine equation x4 + y4 = cz4 In this paper we give sharp explicit estimates for the difference of the Weil height and the Néron  Tate height on the elliptic curve $v^2 = u^3  cu$. We then apply this in the proof of the fact that if c > 2 is a fourth ...

20110920BuchHigher Order OperatorSplitting Methods via Zassenhaus product formula Theory and ApplicationsIn this paper, we contribute higher order operatorsplitting method improved by Zassenhaus product. We apply the contribution to classical and iterative splitting methods. The underlying analysis to obtain higher order ...

20060910BuchHow fast is fast fictitious play? We present a modification of the fictitious play algorithm for matrix games by aggregating trivial original steps. The resulting new algorithm consists of comparable simple steps but has a much better rate of convergence. ...

20051026BuchHow Floquettheory applies to differentialalgebraic equations Local stability of periodic solutions is established by means of a corresponding Floquettheory for index1 differentialalgebraic equations. For this, linear differentialalgebraic equations with periodic coefficients are ...

20051102BuchImproved linear multistep methods for stochastic ordinary differential equations We consider linear multistep methods for stochastic ordinary differential equations and study their convergence properties for problems with small noise or additive noise. We present schemes where the drift part is ...

20110811BuchIn memoriam Richard Mises

20110811BuchInclusions in general spaces Hoelder stability, Solution schemes and Ekeland's principleWe present two basic lemmas on exact and approximate solutions of inclusions and equations in general spaces. Its applications involve Ekeland’s principle, characterize calmness, lower semicontinuity and the Aubin property ...

20051103BuchIndex criteria for differential algebraic equations arising from linearquadratic optimal control problems The index of DAE systems arising from linear quadratic optimal control problems is considered. Necessary and sufficient conditions ensuring regularity with tractability index one are proved. For problems with regular index ...