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
1285.
Günther, Michael
Preconditioned splitting in dynamic iteration schemes for coupled DAE systems in RC network design
In Buikis, Andris and Čiegis, Raimondas and Fitt, Alistair D., Editor, Progress in Industrial Mathematics at ECMI 2002ausThe European Consortium for Mathematics in Industry, Seite 173–177
In Buikis, Andris and Čiegis, Raimondas and Fitt, Alistair D., Editor
Herausgeber: Springer Berlin Heidelberg
20041284.
Günther, Michael
Preconditioned splitting in dynamic iteration schemes for coupled DAE systems in RC network design
In Buikis, Andris and Čiegis, Raimondas and Fitt, Alistair D., Editor, Progress in Industrial Mathematics at ECMI 2002ausThe European Consortium for Mathematics in Industry, Seite 173–177
In Buikis, Andris and Čiegis, Raimondas and Fitt, Alistair D., Editor
Herausgeber: Springer Berlin Heidelberg
20041283.
Günther, Michael
Preconditioned splitting in dynamic iteration schemes for coupled dae systems in rc network design
Progress in Industrial Mathematics at ECMI 2002, Seite 173--177
Springer Berlin Heidelberg
20041282.
Kirsch, Stefan; Ackermann, Olaf; Harms, Klaus; Bach, Thorsten
Regioselective Isomerisation of Highly Substituted 1-Methylenecyclohexenepoxides to the Corresponding Allylic Alcohols. Influence of the Base and of the Protecting Groups
Monatshefte für Chemie / Chemical Monthly, 135 (6) :713–727
2004
ISSN: 1434-44751281.
Borkowska-Burnecka, J.; Zyrnicki, W.; Setzer, Klaus-Dieter; Fink, Ewald H.
Rotational and vibrational temperatures measured in a chemiluminescent flame from FTIR Bi\(_{2}\) emission spectra
Journal of Quantitative Spectroscopy and Radiative Transfer, 86 (1) :87-95
2004
Herausgeber: Pergamon1280.
Borkowska-Burnecka, J.; Zyrnicki, W.; Setzer, Klaus-Dieter; Fink, Ewald H.
Rotational and vibrational temperatures measured in a chemiluminescent flame from FTIR Bi\(_{2}\) emission spectra
Journal of Quantitative Spectroscopy and Radiative Transfer, 86 (1) :87-95
2004
Herausgeber: Pergamon1279.
Borkowska-Burnecka, J.; Zyrnicki, W.; Setzer, Klaus-Dieter; Fink, Ewald H.
Rotational and vibrational temperatures measured in a chemiluminescent flame from FTIR Bi2 emission spectra
Journal of Quantitative Spectroscopy and Radiative Transfer, 86 (1) :87-95
2004
Herausgeber: Pergamon1278.
Scientific Computing in Electrical Engineering -- Proceedings of the SCEE-2002 conference held in Eindhoven
In Schilders, W. H. A. and ter Maten, E. J. W. and Houben, S. H. M. J., Editor, Band 4 aus Mathematics in Industry
Herausgeber: Springer Berlin Heidelberg
2004ISBN: 3540213724
1277.
Appel, Matthew F.; McKeachie, J. Ryan; Veer, Wytze E.; Benter, Thorsten
Simple induction probe electric field meter for the detection of electrical fields generated by ion-optical electrodes
Review of Scientific Instruments, 75 (8) :2603-2607
20041276.
Appel, Matthew F.; McKeachie, J. Ryan; Veer, Wytze E.; Benter, Thorsten
Simple induction probe electric field meter for the detection of electrical fields generated by ion-optical electrodes
Review of Scientific Instruments, 75 (8) :2603-2607
20041275.
Appel, Matthew F.; McKeachie, J. Ryan; van der Veer, Wytze E.; Benter, Thorsten
Simple induction probe electric field meter for the detection of electrical fields generated by ion-optical electrodes
Review of Scientific Instruments, 75 (8) :2603-2607
20041274.
Ehrhardt, M.; Mickens, R. E.
Solutions to the Discrete {Airy} Equation: Application to Parabolic Equation Calculations
JCAM, 172 (1) :183--206
20041273.
Ehrhardt, Matthias
Solutions to the discrete Airy equation: Application to parabolic equation calculations
Journal of Computational and Applied Mathematics, 172 (1) :183–206
2004
Herausgeber: North-Holland1272.
Ehrhardt, Matthias
Solutions to the discrete Airy equation: Application to parabolic equation calculations
Journal of computational and applied mathematics, 172 (1) :183--206
2004
Herausgeber: Elsevier1271.
Winkin, Joseph J.; Callier, Frank M.; Jacob, Birgit; Partington, Jonathan R.
Spectral factorization by symmetric extraction for distributed parameter systems
SIAM J. Control Optim., 43 (4) :1435--1466
20041270.
Winkler, R.
Stochastic {DAEs} in Transient Noise Simulation
In Schilders, W. and ter Maten, J. and Houben, S., Editor, Scientific Computing in Electrical Engineering at SCEE 2002, Seite 408--415
In Schilders, W. and ter Maten, J. and Houben, S., Editor
Herausgeber: Springer
20041269.
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, Berlin
