Browsing by Author "Winkler, Renate"

Now showing items 1-12 of 12

2005-11-03Buch

Asymptotic mean-square stability of two-step methods for stochastic ordinary differential equations

Buckwar, Evelyn; Horváth-Bokor, Rosza; Winkler, Renate

We deal with linear multi-step methods for SDEs and study when the numerical appro\-xi\-mation shares asymptotic properties in the mean-square sense of the exact solution. As in deterministic numerical analysis we use a ...
2005-10-26Buch

How Floquet-theory applies to differential-algebraic equations

Lamour, René; März, Roswitha; Winkler, Renate

Local stability of periodic solutions is established by means of a corresponding Floquet-theory for index-1 differential-algebraic equations. For this, linear differential-algebraic equations with periodic coefficients are ...
2005-11-02Buch

Improved linear multi-step methods for stochastic ordinary differential equations

Buckwar, Evelyn; Winkler, Renate

We consider linear multi-step 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 ...
2006-01-01Buch

Local Error Estimates for Moderately Smooth ODEs and DAEs

Sickenberger, Thorsten; Weinmüller, Ewa; Winkler, Renate

We 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 differential-algebraic equations (DAEs). The ...
2011-07-13Buch

Local error estimates for moderately smooth problems

Part II : SDEs and SDAEs with small noise

Sickenberger, Thorsten; Weinmüller, Ewa; Winkler, Renate

The 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 ...
2005-11-03Buch

Multi-step Maruyama methods for stochastic delay differential equations

Buckwar, Evelyn; Winkler, Renate

In this paper the numerical approximation of solutions of It{\^o} stochastic delay differential equations is considered. We construct stochastic linear multi-step Maruyama methods and develop the fundamental numerical ...
2005-11-03Buch

Multi-step methods for SDEs and their application to problems with small noise

Buckwar, Evelyn; Winkler, Renate

In 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 ...
2005-11-07Buch

On logarithmic norms for differential algebraic equations

Winkler, Renate

Logarithmic 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 ...
2005-11-15Buch

Stability of periodic solutions of index-2 differential algebraic systems

Lamour, René; März, Roswitha; Winkler, Renate

This paper deals with periodic index-2 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 ...
2005-11-03Buch

Stepsize control for mean-square numerical methods for stochastic differential equations with small noise

Römisch, Werner; Winkler, Renate

A strategy for controlling the stepsize in the numerical integration of stochastic differential equations (SDEs) is presented. It is based on estimating the p-th mean of local errors. The strategy leads to deterministic ...
2005-11-03Buch

Stochastic DAEs in Circuit Simulation

Römisch, Werner; Winkler, Renate

Stochastic differential-algebraic 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 ...
2005-11-04Buch

Stochastic Differential Algebraic Equations of index 1 and Applications in Circuit Simulation

Winkler, Renate

Diese Arbeit widmet sich der Untersuchung von Algebro-Differentialgleichungen mit Index 3. Im ersten Kapitel werden grundlegende Begriffe und die Definition der DAE mit Index3 eingefürt. Dabei wird eine spezielle Kette von ...