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
- 1996
662.
Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Towle, J. P.; Brown, John M.
High-Resolution Study of the X\(_{2}\)1 → X\(_{1}\)0\(^{+}\) Fine-Structure Transition of BiF
Journal of Molecular Spectroscopy, 178 (2) :143-156
1996
Herausgeber: Academic Press661.
Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Towle, J. P.; Brown, John M.
High-Resolution Study of the X\(_{2}\)1 → X\(_{1}\)0\(^{+}\) Fine-Structure Transition of BiF
Journal of Molecular Spectroscopy, 178 (2) :143-156
1996
Herausgeber: Academic Press660.
Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Towle, J. P.; Brown, John M.
High-Resolution Study of the X21 → X10+ Fine-Structure Transition of BiF
Journal of Molecular Spectroscopy, 178 (2) :143-156
1996
Herausgeber: Academic Press659.
Becker, Karl Heinz; Geiger, Harald; Wiesen, Peter
Kinetics of the reaction CH + N\(_{2}\) [M]→ Products in the range 10-620 torr and 298-1059 K
International Journal of Chemical Kinetics, 28 (2) :115-123
1996658.
Becker, Karl Heinz; Geiger, Harald; Wiesen, Peter
Kinetics of the reaction CH + N\(_{2}\) [M]→ Products in the range 10-620 torr and 298-1059 K
International Journal of Chemical Kinetics, 28 (2) :115-123
1996657.
Becker, Karl Heinz; Geiger, Harald; Wiesen, Peter
Kinetics of the reaction CH + N2 [M]→ Products in the range 10-620 torr and 298-1059 K
International Journal of Chemical Kinetics, 28 (2) :115-123
1996656.
G\"unther, Michael; Denk, G.; Feldmann, U.
Modeling and simulating charge sensitive {MOS} circuits
Math. Modelling of Systems, 2 :69--81
1996655.
Günther, Michael; Denk, Georg; Feldmann, Uwe
Modeling and simulating charge sensitive MOS circuits
Mathematical Modelling of Systems, 2 (1) :69–81
1996
Herausgeber: Taylor & Francis654.
Denk, G; Feldmann, U
Modelling and simulating charge sensitive MOS circuits
Mathematical Modelling of Systems, 2 (1) :69--81
1996
Herausgeber: Taylor \& Francis653.
Günther, Michael; Hoschek, Markus
Modified ROW methods for electric circuit simulation packages
Preprint (1864)
1996
Herausgeber: Technische Hochschule Darmstadt652.
Günther, Michael
Numerical solution of differential-algebraic equations in electric circuit simulation
In Neunzert, Helmut, Editor
Seite 285–294
Herausgeber: Vieweg+ Teubner
1996
285–294651.
Günther, Michael
Numerical solution of differential-algebraic equations in electric circuit simulation
Progress in Industrial Mathematics at ECMI 94 :285--294
1996
Herausgeber: Vieweg+ Teubner Verlag650.
Denk, Georg; Günther, Michael; Simeon, Bernd
Numerische simulation in chip-design und fahrzeugtechnik
Preprint (1841)
1996
Herausgeber: Technische Hochschule Darmstadt649.
GrÄb, Robert; Günther, Michael; Wever, Utz; Zheng, Qinghua
Optimization of parallel multilevel-Newton algorithms on workstation clusters
In Bougé, Luc and Fraigniaud, Pierre and Mignotte, Anne and Robert, Yves, Editor, Euro-Par96 Parallel ProcessingBand1124ausLecture Notes in Computer Science, Seite 91–96
In Bougé, Luc and Fraigniaud, Pierre and Mignotte, Anne and Robert, Yves, Editor
Herausgeber: Springer Berlin Heidelberg
1996648.
GrÄb, Robert; Günther, Michael; Wever, Utz; Zheng, Qinghua
Optimization of parallel multilevel-Newton algorithms on workstation clusters
In L. Bouge and et al., Editor, Euro-Par'96 Parallel Processing: Second International Euro-Par Conference Lyon, France, August 26--29, 1996 Proceedings, Volume II 2Band1124ausLecture Notes in Computer Science, Seite 91--96
Springer Berlin Heidelberg
In L. Bouge and et al., Editor
Herausgeber: Berlin, Springer-Verlag
1996647.
Klamroth, Kathrin; Mengersen, Ingrid
Ramsey numbers of K_3 versus (p,q)-graphs
Ars Combinatoria, 43 :107-120
1996646.
Becker, Karl Heinz; Kleffmann, Jörg; Kurtenbach, Ralf; Wiesen, Peter
Solubility of nitrous acid (HONO) in sulfuric acid solutions
Journal of Physical Chemistry, 100 (36) :14984-14990
1996645.
Becker, Karl Heinz; Kleffmann, J{ö}rg; Kurtenbach, Ralf; Wiesen, Peter
Solubility of nitrous acid (HONO) in sulfuric acid solutions
Journal of Physical Chemistry, 100 (36) :14984-14990
1996644.
Becker, Karl Heinz; Kleffmann, J{ö}rg; Kurtenbach, Ralf; Wiesen, Peter
Solubility of nitrous acid (HONO) in sulfuric acid solutions
Journal of Physical Chemistry, 100 (36) :14984-14990
1996643.
Tausch, Michael W.; Wachtendonk, M.; Porth, H.-R.; Schulze, I.; Wambach, H.
STOFF-FORMEL-UMWELT, CHEMIE S I
Herausgeber: C. C. Buchner, Bamberg
1996642.
G\"unther, Michael; Rentrop, P.
The {NAND-gate} -- a benchmark for the numerical simulation of digital circuits
In W.~Mathis and P.~Noll, Editor, 2.ITG-Diskussionssitzung ''Neue Anwendungen Theoretischer Konzepte in der Elektrotechnik - mit Gedenksitzung zum 50. Todestag von Wilhelm Cauer'', Seite 27--33
In W.~Mathis and P.~Noll, Editor
Herausgeber: Berlin, VDE-Verlag
1996641.
Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\) → X\(^{3}\)\(\Sigma\)\(^{-}\) Transitions of AsH and AsD
Journal of Molecular Spectroscopy, 178 (2) :165-171
1996
Herausgeber: Academic Press640.
Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\) → X\(^{3}\)\(\Sigma\)\(^{-}\) Transitions of AsH and AsD
Journal of Molecular Spectroscopy, 178 (2) :165-171
1996
Herausgeber: Academic Press639.
Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\) → X\(^{3}\)\(\Sigma\)\(^{-}\) transitions of PH and PD
Chemical Physics Letters, 249 (3-4) :183-190
1996638.
Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\) → X\(^{3}\)\(\Sigma\)\(^{-}\) transitions of PH and PD
Chemical Physics Letters, 249 (3-4) :183-190
1996
