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20051103BuchAsymptotic meansquare stability of twostep methods for stochastic ordinary differential equations Buckwar, Evelyn; HorváthBokor, Rosza; Winkler, RenateWe deal with linear multistep methods for SDEs and study when the numerical appro\xi\mation shares asymptotic properties in the meansquare sense of the exact solution. As in deterministic numerical analysis we use a ...

20051026BuchHow Floquettheory applies to differentialalgebraic equations Lamour, René; März, Roswitha; Winkler, RenateLocal 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 Buckwar, Evelyn; Winkler, RenateWe 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 ...

20060101BuchLocal Error Estimates for Moderately Smooth ODEs and DAEs Sickenberger, Thorsten; Weinmüller, Ewa; Winkler, RenateWe discuss an error estimation procedure for the local errors of low order methods applied to solve initial value problems in ordinary differential equations (ODEs) and index 1 differentialalgebraic equations (DAEs). The ...

20110713BuchLocal error estimates for moderately smooth problems Part II : SDEs and SDAEs with small noiseSickenberger, Thorsten; Weinmüller, Ewa; Winkler, RenateThe paper consists of two parts. In the first part of the paper, we proposed a procedure to estimate local errors of low order methods applied to solve initial value problems in ordinary differential equations (ODEs) and ...

20051103BuchMultistep Maruyama methods for stochastic delay differential equations Buckwar, Evelyn; Winkler, RenateIn this paper the numerical approximation of solutions of It{\^o} stochastic delay differential equations is considered. We construct stochastic linear multistep Maruyama methods and develop the fundamental numerical ...

20051103BuchMultistep methods for SDEs and their application to problems with small noise Buckwar, Evelyn; Winkler, RenateIn this paper the numerical approximation of solutions of Ito stochastic differential equations is considered, in particular for equations with a small parameter $\epsilon$ in the noise coefficient. We construct stochastic ...

20051107BuchOn logarithmic norms for differential algebraic equations Winkler, RenateLogarithmic matrix norms are well known in the theory of ordinary differential equations (ODEs) where they supply estimates for error growth and the growth of the solutions. In this paper we present a natural generalization ...

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 ...

20051103BuchStepsize control for meansquare numerical methods for stochastic differential equations with small noise Römisch, Werner; Winkler, RenateA strategy for controlling the stepsize in the numerical integration of stochastic differential equations (SDEs) is presented. It is based on estimating the pth mean of local errors. The strategy leads to deterministic ...

20051103BuchStochastic DAEs in Circuit Simulation Römisch, Werner; Winkler, RenateStochastic differentialalgebraic equations (SDAEs) arise as a mathematical model for electrical network equations that are influenced by additional sources of Gaussian white noise. We sketch the underlying analytical ...

20051104BuchStochastic Differential Algebraic Equations of index 1 and Applications in Circuit Simulation Winkler, RenateDiese 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 ...