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: 1312.
Yamada, Koichi M. T.; Winnewisser, Gisbert; Jensen, Per
Internal rotation tunnelling in HSOH
Journal of Molecular Structure, 695-696 :323-337
2004
Herausgeber: Elsevier
DOI: 10.1016/j.molstruc.2003.12.042; 1311.
Yamada, Koichi M. T.; Winnewisser, Gisbert; Jensen, Per
Internal rotation tunnelling in HSOH
Journal of Molecular Structure, 695-696 :323-337
2004
Herausgeber: Elsevier
DOI: 10.1016/j.molstruc.2003.12.042; 1310.
Yamada, Koichi M. T.; Winnewisser, Gisbert; Jensen, Per
Internal rotation tunnelling in HSOH
Journal of Molecular Structure, 695-696 :323-337
2004
Herausgeber: Elsevier
DOI: 10.1016/j.molstruc.2003.12.042; 1309.
Kevenaar, T. A. M.; Maten, E. J. W.; Janssen, H. H. J. M.; Onneweer, S. P.
Methods and Approaches for {RF} Circuit Simulation and Electromagnetic Modelling
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 29--45
Herausgeber: Springer Berlin Heidelberg
2004
29--45
DOI: 10.1007/978-3-642-55872-6_3; 1308.
Allaart-Bruin, Sandra; Maten, Jan; Lunel, Sjoerd Verduyn
Modified Extended {BDF} Time-Integration Methods, Applied to Circuit Equations
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 86--93
Herausgeber: Springer Berlin Heidelberg
2004
86--93
DOI: 10.1007/978-3-642-55872-6_7; 1307.
Overman, Larry E.; Watson, Mary P.
Monomeric Cobalt Oxazoline Palladacycles (COP). Useful Catalysts for Catalytic Asymmetric Rearrangement of Allylic Trichloroacetimidates
The Journal of Organic Chemistry, 69 (23) :8101–8104
2004
ISSN: 0022-3263, 1520-6904
DOI: 10.1021/jo0487092; 1306.
Ali, G.; Bartel, A.
Multi-physics models in electric circuit design
In R. Monaco and S. Pennisi and S. Rionero and T. Ruggeri, Editor, Proceedings ’WASCOM 2003’ 12th Conference on Waves and Stability in Continuous Media, World Scientific Publishing, Singapore, 2004, Seite 1--6
In R. Monaco and S. Pennisi and S. Rionero and T. Ruggeri, Editor
2004; 1305.
Ali, G; Bartel, A
MULTI-PHYSICS MODELS IN ELECTRIC NETWORK DESIGN
Waves And Stability In Continuous Media, Proceedings of WASCOM 2003, Seite 1--6
Herausgeber: World Scientific
2004; 1304.
Alì, Giuseppe; Bartel, Andreas
Multi-physics models in electric network design
Seite 1–6
Herausgeber: World Scientific Publishing
2004
1–6
DOI: 10.1142/9789812702937_0001; 1303.
Bartel, Andreas; Günther, Michael
Multirate co-simulation of first order thermal models in electric circuit design
In Schilders, Wilhelmus H. A. and ter Maten, E. Jan W. and Houben, Stephan H. M. J., Editor, Scientific Computing in Electrical Engineering: Proceedings of the SCEE-2002 Conference held in EindhovenausMathematics in Industry, Seite 104–111
In Schilders, Wilhelmus H. A. and ter Maten, E. Jan W. and Houben, Stephan H. M. J., Editor
Herausgeber: Springer Berlin Heidelberg
2004
DOI: 10.1007/978-3-642-55872-6_9; 1302.
Bartel, Andreas; Günther, Michael
Multirate co-simulation of first order thermal models in electric circuit design
In W.H.A. Schilders and et al., Editor, Scientific Computing in Electrical Engineering: Proceedings of the SCEE-2002 Conference held in Eindhoven, Seite 104--111
Springer Berlin Heidelberg
In W.H.A. Schilders and et al., Editor
Herausgeber: Springer-Verlag, Berlin
2004; 1301.
Bartel, Andreas; Günther, Michael
Multirate co-simulation of first order thermal models in electric circuit design
In Schilders, Wilhelmus H. A. and ter Maten, E. Jan W. and Houben, Stephan H. M. J., Editor, Scientific Computing in Electrical Engineering: Proceedings of the SCEE-2002 Conference held in EindhovenausMathematics in Industry, Seite 104–111
In Schilders, Wilhelmus H. A. and ter Maten, E. Jan W. and Houben, Stephan H. M. J., Editor
Herausgeber: Springer Berlin Heidelberg
2004
DOI: 10.1007/978-3-642-55872-6_9; 1300.
Steinbacher, M.; Henne, S.; Dommen, J.; Wiesen, Peter; Pr{é}v{{\^o}}t, Andre S. H.
Nocturnal trans-alpine transport of ozone and its effects on air quality on the Swiss Plateau
Atmospheric Environment, 38 (27) :4539-4550
2004
Herausgeber: Pergamon
DOI: 10.1016/J.ATMOSENV.2004.05.008; 1299.
Steinbacher, M.; Henne, S.; Dommen, J.; Wiesen, Peter; Pr{é}v{{\^o}}t, Andre S. H.
Nocturnal trans-alpine transport of ozone and its effects on air quality on the Swiss Plateau
Atmospheric Environment, 38 (27) :4539-4550
2004
Herausgeber: Pergamon
DOI: 10.1016/J.ATMOSENV.2004.05.008; 1298.
Steinbacher, M.; Henne, S.; Dommen, J.; Wiesen, Peter; Prévôt, Andre S. H.
Nocturnal trans-alpine transport of ozone and its effects on air quality on the Swiss Plateau
Atmospheric Environment, 38 (27) :4539-4550
2004
Herausgeber: Pergamon
DOI: 10.1016/J.ATMOSENV.2004.05.008; 1297.
McKeachie, J. Ryan; Appel, Matthew F.; Kirchner, Ulf; Schindler, Ralph N.; Benter, Thorsten
Observation of a heterogeneous source of OClO from the reaction of ClO radicals on ice
Journal of Physical Chemistry B, 108 (43) :16786-16797
2004
DOI: 10.1021/jp049314p; 1296.
McKeachie, J. Ryan; Appel, Matthew F.; Kirchner, Ulf; Schindler, Ralph N.; Benter, Thorsten
Observation of a heterogeneous source of OClO from the reaction of ClO radicals on ice
Journal of Physical Chemistry B, 108 (43) :16786-16797
2004
DOI: 10.1021/jp049314p; 1295.
McKeachie, J. Ryan; Appel, Matthew F.; Kirchner, Ulf; Schindler, Ralph N.; Benter, Thorsten
Observation of a heterogeneous source of OClO from the reaction of ClO radicals on ice
Journal of Physical Chemistry B, 108 (43) :16786-16797
2004
DOI: 10.1021/jp049314p; 1294.
Buckwar, E.; Winkler, R.
On two-step schemes for SDEs with small noise
PAMM, 4 (1) :15-18
2004; 1293.
Bartel, Andreas
Partial differential algebraic models in chip design — thermal and semiconductor problems
2004
Download; 1292.
Bartel, Andreas
Partial Differential Algebraic Models in Chip Design-Thermal and Semiconductor Problems
Herausgeber: VDI-Verlag
2004; 1291.
Bartel, A.:
Partial Differential-Algebraic Models in Chip-Design — Thermal and Semiconductor Problems
TU Munich, Fortschritt-Berichte, VDI Verlag, Düsseldorf
2004; 1290.
Farkas, Bálint
Perturbations of bi-continuous semigroups with applications to transition semigroups on C\sb b(H)
Semigroup Forum, 68 (1) :87-107
2004
DOI: 10.1007/s00233-002-0024-2; 1289.
Melnikov, Vladlen V.; Jensen, Per
Potential energy surface and spectroscopic parameters of X\verb=~=\(^{3}\)\(\Sigma\)\(^{-}\) CNN
Chemical Physics Letters, 394 (1-3) :171-175
2004
DOI: 10.1016/j.cplett.2004.06.129; 1288.
Melnikov, Vladlen V.; Jensen, Per
Potential energy surface and spectroscopic parameters of X\verb=~=\(^{3}\)\(\Sigma\)\(^{-}\) CNN
Chemical Physics Letters, 394 (1-3) :171-175
2004
DOI: 10.1016/j.cplett.2004.06.129

Index Analysis

Group members working on that field

Cooperations

Publications

1312.

1311.

1310.

1309.

1308.

1307.

1306.

1305.

1304.

1303.

1302.

1301.

1300.

1299.

1298.

1297.

1296.

1295.

1294.

1293.

1292.

1291.

1290.

1289.

1288.