Renate Winkler

Publications in refereed journals and book

E.  Buckwar, A. Rößler and R. Winkler:
Runge-Kutta Methods for SDEs with Small Noise,
SIAM J. Sci. Comp. vol. 32 (4) (2010), 1789--1808.

W. Römisch, T. Sickenberger und R. Winkler:
Simultaneous step-size and path control for efficient transient noise analysis. [prepress]
In J. Roos, L.R. Costa (Eds.), Scientific Computing in Electrical Engineering SCEE 2008 (Helsinki),
Springer, Berlin (2010), 167-174.
ISBN: 978-3-642-12293-4, [springer.de, amazon.de, amazon.com]

T. Sickenberger,  E. Weinmüller  and R. Winkler:
Local error estimates for moderately smooth problems: Part II - SDEs and SDAEs with small noise. [preprint 07-07],
BIT Numerical Mathematics vol. 49(1) (2009), pp. 217 - 245.

T. Sickenberger and R. Winkler:
Stochastic oscillations in circuit simulation, [prepress]
PAMM vol. 7(1) (2008),  4050023-4050024.

G. Denk, W. Römisch, T.  Sickenberger, and R. Winkler:
Efficient transient noise analysis in circuit simulation, [prepress]
In W. Jäger and H.-J. Krebs (Eds.): Mathematics - Key Technology for the Future, Springer, Berlin (2008),  39-49.
ISBN: 978-3-540-77202-6, [springer.de, amazon.de, amazon.com]

T. Sickenberger and R. Winkler:
Adaptive Methods for Transient Noise Analysis, [prepress]
In G. Ciuprina, D. Ioan (Eds.), Scientific Computing in Electrical Engineering SCEE 2006,
Springer, Berlin (2007), 403-410.
ISBN: 978-3-540-71979-3, [springer.de, amazon.de, amazon.com

T. Sickenberger, E. Weinmüller  and R. Winkler:
Local error estimates for moderately smooth problems: Part I - ODEs and DAEs, [preprint 06-01],
BIT Numerical Mathematics vol. 47(1) (2007),  157 - 187.

W. Römisch, T. Sickenberger und R. Winkler:
Mathematik - Grips für Chips: Effiziente transiente Rauschanalyse in der Schaltungssimulation [in german],
in Der Schlüssel zur Hochtechnologie - Mathematik für Innovationen in Industrie und Diensteistungen, BMBF, 2007.

E. Buckwar and R. Winkler:
Multi-step Maruyama methods for stochastic delay differential equations,
Stoch. Anal. Appl. vol. 25 (5) (2007),  933--959.

E. Buckwar and R. Winkler:
Improved linear multi-step methods for stochastic ordinary differential equations,

J. Comp. Appl. Math. vol. 205 (2) (2007),  912--922.

E. Buckwar, R. Horvath Bokor and R. Winkler:
Asymptotic mean-square stability of two-step methods for stochastic ordinary differential equations,
BIT Numerical Mathematics vol. 46 (2) (2006), 261 - 282.

T. Sickenberger and R. Winkler:
Efficient transient noise analysis in circuit simulation
PAMM vol. 6 (1) (2006),  55-58.

E. Buckwar and R.Winkler:
Improved Linear Multi-step Methods for Small Noise SDEs

PAMM, vol. 6 (1) ( 2006), 661--662.

E. Buckwar and R.Winkler:
Asymptotic Mean-square Stability of Linear Multi-step Methods for SODEs,
PAMM, vol. 6 (1) ( 2006), 659--660.

W. Römisch and R. Winkler:
Stepsize control for mean-square numerical methods for stochastic differential equations with small noise,
SIAM J. Sci. Comp. vol. 28 (2) (2006), 604-625.

E. Buckwar and R.Winkler:
Multi-step methods for SDEs and their application to problems with small noise,
SIAM J. Num. Anal. vol. 44 (2)  (2006), 779--803.

R.Winkler:
Stochastic differential algebraic equations  in transient noise analysis,
Springer Series 'Mathematics in Industry' ,Proceedings of 'Scientific Computing in Electrical Engineering', September, 25th - 9th, 2004, Capo D'Orlando,  151-158.

E. Buckwar and R.Winkler:
On two-step schemes for SDEs with small noise,

PAMM, vol. 4 (1) ( 2004), 15-18.

W. Römisch and R. Winkler:
Stochastic DAEs in circuit simulation,

in:  Mathematical Modeling, Simulation and Optimization of Integrated Circuits (Eds.) K.Antreich, R.Bulirsch, A. Gilg and P. Rentrop,  Birkhäuser, 2003, 303-318.

G. Denk and R.Winkler:
Modeling and simulation of transient noise in circuit simulation,

Proceedings of 4th MATHMOD, Vienna, Feb. 5-7, 2003, to appear in: Mathematical and Computer Modelling of Dynamical Systems (MCMDS).

R.Winkler:
Stochastic differential algebraic equations of index 1 and applications in circuit simulation,
J. Comp. Appl. Math. 157 (2003), 477-505.

R. Lamour, R. März and R.Winkler:
Stability of periodic solutions of index-2 differential-algebraic systems
,
J. Math. Anal. Appl.. 279 (2003), 475-494.

R.Winkler:
Stochastic DAEs in transient noise simulation,
Springer Series 'Mathematics in Industry' ,Proceedings of 'Scientific Computing in Electrical Engineering', June, 23rd - 28th, 2002, Eindhoven, 408-415.

R. Lamour, R. März and R.Winkler:
How Floquet theory applies to index 1 differential algebraic equations,

J. Math. Anal. Appl. 217 (1998), 372--394.


Preprints

T. Sickenberger, E. Weinmüller  and R. Winkler: Local error estimates for moderately smooth ODEs and DAEs,
Preprint 06-1, Institut für Mathematik, Humboldt-Universität Berlin, 2006

E. Buckwar and R. Winkler: Improved linear multi-step methods for stochastic ordinary differential equations,
Preprint 05-10, Institut für Mathematik, Humboldt-Universität Berlin, 2005

E. Buckwar, R. Horvath Bokor and R. Winkler: Asymptotic mean-square stability of two-step methods for stochastic ordinary differential equations,
Preprint 04-25, Institut für Mathematik, Humboldt-Universität Berlin, 2004.

E. Buckwar and R. Winkler: Multi-step Maruyama methods for stochastic delay differential equations,
Preprint 04-15, Institut für Mathematik, Humboldt-Universität Berlin, 2004.

E. Buckwar and R.Winkler: Multi-step methods for SDEs and their application to problems with small noise,
Preprint 03-17, Institut für Mathematik, Humboldt-Universität Berlin, 2003.

W. Römisch and R. Winkler: Stepsize control for mean-square numerical methods for stochastic differential equations with small noise,
Preprint 03-8, Institut für Mathematik,  Humboldt-Universität Berlin, 2003.

W. Römisch and R. Winkler: Stochastic DAEs in circuit simulation,
Preprint 03-03, Institut für Mathematik, Humboldt-Universität Berlin, 2003.

R.Winkler: Stochastic differential algebraic equations of index 1 and applications in circuit simulation,
Preprint 01-13  Institut für Mathematik, Humboldt-Universität Berlin, 2001.

R. Winkler: On logarithmic norms for differential algebraic equations,
Preprint 00-17   Institut für Mathematik, Humboldt-Universität Berlin, 2000.

R. Lamour, R. März and R.Winkler: Stability of periodic solutions of index-2 differential-algebraic systems,
Preprint  98-23  Institut für Mathematik, Humboldt-Universität Berlin, 1998.

R. Lamour, R. März and R.Winkler: How Floquet theory applies to differential algebraic equations,
Preprint  96-15  Institut für Mathematik, Humboldt-Universität Berlin, 1996

R. Winkler: On simple impasse points and their numerical computation,
Preprint  94-15  Institut für Mathematik, Humboldt-Universität Berlin, 1994