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
- 2004
1269.
Kahl, Christian; Günther, Michael; Roßberg, Thilo
Structure preserving stochastic integration schemes in interest rate derivative modeling
Applied Numerical Mathematics, 58 (3) :284--295
2004
Herausgeber: North-Holland1268.
Rommes, J.; Bomhof, C. W.; Vorst, H. A.; Maten, E. J. W.
The Application of Preconditioned {Jacobi-Davidson} Methods in Pole-zero Analysis
In W. H. A. Schilders and E. J. W. ter Maten and S. H. M. J. Houben, Editor, Scientific Computing in Electrical Engineering at SCEE 2002, Eindhoven Band 4 aus Mathematics in Industry
Seite 349--355
Herausgeber: Springer Berlin Heidelberg
2004
349--3551267.
Abel, Ulrich; Heilmann, Margareta
The complete asymptotic expansion for Bernstein-Durrmeyer operators with Jacobi weights
Mediterranean Journal of Mathematics, 1 (4) :487-499
20041266.
Yurchenko, Sergey N.; Bunker, Philip R.; Kraemer, Wolfgang P.; Jensen, Per
The spectrum of singlet SiH\(_{2}\)
Canadian Journal of Chemistry, 82 (6) :694-708
2004
Herausgeber: NRC Research Press Ottawa, Canada1265.
Yurchenko, Sergey N.; Bunker, Philip R.; Kraemer, Wolfgang P.; Jensen, Per
The spectrum of singlet SiH\(_{2}\)
Canadian Journal of Chemistry, 82 (6) :694-708
2004
Herausgeber: NRC Research Press Ottawa, Canada1264.
Yurchenko, Sergey N.; Bunker, Philip R.; Kraemer, Wolfgang P.; Jensen, Per
The spectrum of singlet SiH2
Canadian Journal of Chemistry, 82 (6) :694-708
2004
Herausgeber: NRC Research Press Ottawa, Canada1263.
Bartel, A
Thermal Models in Electric Circuit Design
, Scientific Computing in Electrical Engineering: Proceedings of the SCEE-2002 Conference held in EindhovenBand4, Seite 104
Springer Science & Business Media
20041262.
Striebel, M
Towards One-Step Multirate Methods in Chip Design
Preprint IMACM
2004
Herausgeber: Bergische Universität Wuppertal1261.
Striebel, M
Towards One-Step Multirate Methods in Chip Design
:129--126
2004
Herausgeber: Springer-Verlag, Berlin1260.
Striebel, M
Towards One-Step Multirate Methods in Chip Design
Preprint IMACM
2004
Herausgeber: Bergische Universität Wuppertal1259.
Wu, Shenghai; Chen, Yangqin; Yang, Xiaohua; Guo, Yingchun; Liu, Yuyan; Li, Yan; Buenker, Robert J.; Jensen, Per
Vibronic transition moments and line intensities for H\(_{2}\)O\(^{+}\)
Journal of Molecular Spectroscopy, 225 (1) :96-106
2004
Herausgeber: Academic Press1258.
Wu, Shenghai; Chen, Yangqin; Yang, Xiaohua; Guo, Yingchun; Liu, Yuyan; Li, Yan; Buenker, Robert J.; Jensen, Per
Vibronic transition moments and line intensities for H\(_{2}\)O\(^{+}\)
Journal of Molecular Spectroscopy, 225 (1) :96-106
2004
Herausgeber: Academic Press1257.
Wu, Shenghai; Chen, Yangqin; Yang, Xiaohua; Guo, Yingchun; Liu, Yuyan; Li, Yan; Buenker, Robert J.; Jensen, Per
Vibronic transition moments and line intensities for H2O+
Journal of Molecular Spectroscopy, 225 (1) :96-106
2004
Herausgeber: Academic Press1256.
Bohrmann-Linde, Claudia
Von der Elektrolysezelle zur Leuchtdiode - Elektrolumineszenz im Chemieunterricht
Praxis der Naturwissenschaften - Chemie in der Schule, 56 (6)
20041255.
Jacob, Birgit
What is the better signal space for discrete-time systems: l_2(\Bbb Z) or l_2(\Bbb N_0)?
SIAM J. Control Optim., 43 (4) :1521--1534
20041254.
Tausch, Michael W.
Zink - Ein Element von A bis Z
Praxis der Naturwissenschaften - Chemie in der Schule, 53 (7) :1
20041253.
Tausch, Michael W.; Rohe, Bernd
Zinksulfat - Ein technisches Produkt mit didaktisch interessanten Facetten
Praxis der Naturwissenschaften - Chemie in der Schule, 53 (7) :21
2004- 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
2003
