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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 ...

20051107BuchIndex determination of DAEs The index definition of DAEs with properly stated leading term bases on a matrix sequence with suitably chosen projectors. A way of realization of this matrix sequence is presented, it includes the calculation of suitable ...

20020116BuchIndex3 AlgebroDifferentialgleichungen mit proper formuliertem Hauptterm Diese Arbeit widmet sich der Untersuchung von AlgebroDifferentialgleichungen mit Index 3. Im ersten Kapitel werden grundlegende Begriffe und die Definition der DAE mit Index3 eingefürt. Dabei wird eine spezielle Kette von ...

19940301BuchIntegrating Logical Functions with ILF This is a description of the system ILF developed at the HumboldtUniversity at Berlin. ILF is a system that integrates automated theorem provers, proof tactics for interactive deductive systems and models within a graphical ...

20051021BuchInterior Integral Estimates on Weak Solutions of Nonlinear Parabolic Systems This paper concerns various types of CACCIOPPOLI and POINCARÈ inequalities on weak solutions u of nonlinear parabolic systems. The main result of the paper is the local integrability of the spatial gradient Du to an exponent ...

20060802BuchInternal Layer Solutions in Quasilinear IntegroDifferential Equations The Dirichlet boundary value problem for a class of singularly perturbed quasilinear integrodifferential equations is considered. The asymptotic expansion for a new class of solutions, which have internal layers, is ...

20051116BuchIteration methods with incomplete corrections and solution of nonlinear equations Basing on the theory of dynamic systems with inclomplete corrections [12], various methods of GaussSeideltype for the numerical solution of nonlinear equations are formulated and analyzed. For special classes of equations ...