Index Analysis
DAEs are no ODEs. Actually, Differential agebraic equations (DAEs) are a mixture of ordinary differential equations (ODEs) and algebraic relations. This may create difficulties, which are not seen at the first sight. The analysis shows that due this mixture hidden differentiation might occur. Recalling from analysis that differentiation is not an unbounded operator, such a process is much more difficult to handle than the integrals used for solving ODEs. E.g. imagine a sinosoidal signal of small amplitude but with high frequency, such as a numerical error, the derivative is of much larger magnitude.
Clearly, the more derivatives involved in the exact solution of a DAE, the more one needs to be careful in numerical computations. The index is a measure for this difficutly. That is why it is important to know the index before simulation.
Group members working on that field
- Andreas Bartel
- Michael Günther
Cooperations
- Giuseppe Ali (Academia)
- Sascha Baumanns (Academia)
- Caren Tischendorf (Academia)
Publications
- 2003
1252.
Houben, S. H. M. J.; Maten, E. J. W.; Sevat, M.F.
A new transient integration method for free-running oscillators
In R. Vahrmann, Editor, Analog 2003 -- Entwicklung von Analogschaltungen mit CAE-Methoden mit dem Schwerpunkt Entwurfsverfahren für Automotive-Anwendungen, Seite 61-66
In R. Vahrmann, Editor
September 20031251.
Feldmann, Jorg-Uwe; Günther, Michael
Simulation apparatus and simulation method for a system having analog and digital elements
August 20031250.
Tausch, Michael W.; Goodwin, Alan
... zur Forschung in der Didaktik: 7 Thesen ...
Chemie in unserer Zeit, 37 (3) :210--211
2003
Herausgeber: Wiley1249.
[german] Tausch, Michael W.
1 mol Quanten? - Ja bitte, aber blaue
Praxis der Naturwissenschaften - Chemie in der Schule, 52 (7) :23
20031248.
Ehrhardt, Matthias
A fast method to implement non-local discrete transparent boundary conditions for the Schrödinger equation
PAMM: Proceedings in Applied Mathematics and Mechanics, 2 (1) :424–425
2003
Herausgeber: WILEY-VCH Verlag1247.
A fast method to implement non-local discrete transparent boundary conditions for the Schrödinger equation
, PAMM: Proceedings in Applied Mathematics and MechanicsBand2, Seite 424--425
WILEY-VCH Verlag Berlin
20031246.
Günther, Michael
A refined PDAE network model for a CMOS ring oscillator
In Antreich, K. and {et al.}, Editor, Modeling, Simulation, and Optimization of Integrated Circuits: Proceedings of a Conference held at the Mathematisches Forschungsinstitut, Oberwolfach, November 25-December 1, 2001, Seite 203--218
Birkhäuser Basel
In Antreich, K. and {et al.}, Editor
Herausgeber: Birkh\"auser Verlag, Basel
20031245.
Günther, Michael
A refined PDAE network model for a CMOS ring oscillator
In Antreich, Kurt and Bulirsch, Roland and Gilg, Albert and Rentrop, Peter, Editor, Modeling, Simulation and Optimization of Integrated CircuitsausISNM International Series of Numerical Mathematics, Seite 203–218
In Antreich, Kurt and Bulirsch, Roland and Gilg, Albert and Rentrop, Peter, Editor
Herausgeber: Birkhäuser Basel
20031244.
Günther, Michael
A refined PDAE network model for a CMOS ring oscillator
In Antreich, Kurt and Bulirsch, Roland and Gilg, Albert and Rentrop, Peter, Editor, Modeling, Simulation and Optimization of Integrated CircuitsausISNM International Series of Numerical Mathematics, Seite 203–218
In Antreich, Kurt and Bulirsch, Roland and Gilg, Albert and Rentrop, Peter, Editor
Herausgeber: Birkhäuser Basel
20031243.
Jacob, Birgit
An operator theoretical approach towards systems over the signal space l_2(\Bbb Z)
Integral Equations Operator Theory, 46 (2) :189--214
20031242.
Al, Guiseppe; Bartel, Andreas; Günther, Michael
Analysis of coupled systems in chip design
Herausgeber: Universität Karlsruhe, Institut für Wissenschaftliches Rechnen und~…
20031241.
Ehrhardt, Matthias
Approximation, stability and fast calculation of non-local boundary conditions for the Schrödinger equation
Commun. Math. Sci, 1 (3) :501--556
20031240.
Heijmen, T. G. A.; Lin, C.; Maten, E. J. W.; Sevat, M. F.
Augmented Lagrangian Algorithm for Optimizing Analog Circuit Design
In A. Buikis and R. Ciegis and A. D. Fitt, Editor, Progress in Industrial Mathematics at {ECMI} 2002, Jurmala Band 5 aus Mathematics in Industry
Seite 179--184
Herausgeber: Springer Berlin Heidelberg
2003
179--1841239.
Tausch, Michael W.; Wachtendonk, Magdalene; Bohrmann-Linde, Claudia; Krollmann, P.; Schmitz, W.; Wambach, H.
CHEMIE 2000+ Band 2, Lehrbuch für die gymnasiale Oberstufe
Herausgeber: C.C.Buchner, Bamberg
20031238.
Tausch, Michael W.; Szemenyei, M.; Maibaum, R.; al., et
Chemie 2000+ Online - Internet-Portal mit Online-Service für Unterricht und Studium
Online
20031237.
Rentrop, P.; G\"unther, Michael; Hoschek, M.; Feldmann, U.
CHORAL - a charge-oriented algorithm for the numerical integration of electrical circuits
In W. Jäger and H.-J. Krebs, Editor, Mathematics - Key Technology for the Future. Joint Projects Between Universities and Industry
Seite 429-438
Herausgeber: Springer Verlag, Berlin
2003
429-4381236.
Rentrop, P.; Günther, M.; Hoschek, M.; Feldmann, U.
CHORAL - a charge-oriented algorithm for the numerical integration of electrical circuits
In Jäger, WIlli and Krebs, Hans-Joachim, Editor
Seite 429–438
Herausgeber: Springer Berlin Heidelberg
2003
429–4381235.
Rentrop, P.; Günther, M.; Hoschek, M.; Feldmann, U.
CHORAL - a charge-oriented algorithm for the numerical integration of electrical circuits
In Jäger, WIlli and Krebs, Hans-Joachim, Editor
Seite 429–438
Herausgeber: Springer Berlin Heidelberg
2003
429–4381234.
Heilmann, Margareta
Commutativity of Durrmeyer-type modifications of Meyer-König and Zeller and Baskakov-operators
Constructive Theory of Functions - Proceedings of the International Conference, Varna, Bulgaria, 2002, Seite 295-301
In B. Bojanov et al., Editor
Herausgeber: Sofia: DARBA
20031233.
Jacob, Birgit; Partington, Jonathan R.; Pott, Sandra
Conditions for admissibility of observation operators and boundedness of Hankel operators
Integral Equations Operator Theory, 47 (3) :315--338
20031232.
Günther, Michael; Jüngel, Ansgar
Die Monte-Carlo-Methode
Finanzderivate mit MATLAB{\textregistered}: Mathematische Modellierung und numerische Simulation :97--148
2003
Herausgeber: Vieweg+ Teubner Verlag1231.
Tausch, Michael W.; Haas, L.
Die Standard-Matrix, ein Paradigma für den Chemieunterricht
Praxis der Naturwissenschaften - Chemie in der Schule, 52 (1) :7
20031230.
Ehrhardt, Matthias
Discrete transparent boundary conditions for the Schrödinger equation: Fast calculation, approximation, and stability
Communications in Mathematical Sciences, 1 (3) :501–556
2003
Herausgeber: International Press1229.
Ehrhardt, Matthias
Discrete transparent boundary conditions for the Schrödinger equation: fast calculation, approximation, and stability
20031228.
Tausch, Michael W.
Dutzend, Schock... Mol - in eine Schublade?
Praxis der Naturwissenschaften - Chemie in der Schule, 52 (7) :1
2003
