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
- 1998
794.
Jacob, Birgit
A formula for the stability radius of time-varying systems
J. Differential Equations, 142 (1) :167--187
1998793.
Feldmann, Uwe
CAD-based electric-circuit modeling in industry II: Impact of circuit configurations and parameters
Surveys on Mathematics for Industry, 8 (2) :131--158
1998
Herausgeber: Wien; New York: Springer-Verlag, 1991-c2005.792.
Jacob, Birgit; Larsen, Mikael; Zwart, Hans
Corrections and extensions of: ``Optimal control of linear systems with almost periodic inputs" [SIAM J. Control Optim. \bf 25 (1987), no. 4, 1007--1019; MR0893995 (88i:93042)] by G. Da Prato and A. Ichikawa
SIAM J. Control Optim., 36 (4) :1473--1480
1998791.
[german] Tausch, Michael W.; Balzer, M.
Die Ketone und das Licht
Praxis der Naturwissenschaften (Chemie), 47 (7) :14
1998790.
Ehrhardt, Matthias
Discrete transparent boundary conditions for wide angle parabolic equations in underwater
Journal of Computational Physics, 145 :469--470
1998789.
Ehrhardt, Matthias
Discrete Transparent Boundary Conditions For Wide Angle Parabolic Equations In Underwater Acoustics
Journal of Computational Physics, 145 :469-470
1998788.
Ehrhardt, Matthias
Discrete transparent boundary conditions for wide angle parabolic equations in underwater acoustics
Journal of Computational Physics, 145 (2) :611–638
1998
Herausgeber: Elsevier787.
Tausch, Michael W.; Grolmuss, A.; Piwek, B.
Echtfarben-Emissionsspektren EFES - Ein Beitrag zum Verständnis von Licht und Farbe
Praxis der Naturwissenschaften (Chemie), 47 (2) :10
1998786.
Shestakov, Oleg; Breidohr, R.; Demes, H.; Setzer, Klaus-Dieter; Fink, Ewald H.
Electronic States and Spectra of BiO
Journal of Molecular Spectroscopy, 190 (1) :28-77
1998
Herausgeber: Academic Press785.
Shestakov, Oleg; Breidohr, R.; Demes, H.; Setzer, Klaus-Dieter; Fink, Ewald H.
Electronic States and Spectra of BiO
Journal of Molecular Spectroscopy, 190 (1) :28-77
1998
Herausgeber: Academic Press784.
Shestakov, Oleg; Breidohr, R.; Demes, H.; Setzer, Klaus-Dieter; Fink, Ewald H.
Electronic States and Spectra of BiO
Journal of Molecular Spectroscopy, 190 (1) :28-77
1998
Herausgeber: Academic Press783.
Brasseur, G. P.; Cox, R. A.; Hauglustaine, D.; Isaksen, I.; Lelieveld, J.; Lister, D. H.; Sausen, R.; Schumann, Ulrich; Wahner, A.; Wiesen, Peter
European scientific assessment of the atmospheric effects of aircraft emissions
Atmospheric Environment, 32 (13) :2329-2418
1998782.
Brasseur, G. P.; Cox, R. A.; Hauglustaine, D.; Isaksen, I.; Lelieveld, J.; Lister, D. H.; Sausen, R.; Schumann, Ulrich; Wahner, A.; Wiesen, Peter
European scientific assessment of the atmospheric effects of aircraft emissions
Atmospheric Environment, 32 (13) :2329-2418
1998781.
Brasseur, G. P.; Cox, R. A.; Hauglustaine, D.; Isaksen, I.; Lelieveld, J.; Lister, D. H.; Sausen, R.; Schumann, Ulrich; Wahner, A.; Wiesen, Peter
European scientific assessment of the atmospheric effects of aircraft emissions
Atmospheric Environment, 32 (13) :2329-2418
1998780.
Shestakov, Oleg; Gielen, R.; Setzer, Klaus-Dieter; Fink, Ewald H.
Gas phase LIF study of the b\(^{1}\)\(\Sigma\)\(^{+}\)(b0\(^{+}\)) ↔ X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{1}\)0\(^{+}\),X\(_{2}\)1) transition of NI
Journal of Molecular Spectroscopy, 192 (1) :139-147
1998
Herausgeber: Academic Press779.
Shestakov, Oleg; Gielen, R.; Setzer, Klaus-Dieter; Fink, Ewald H.
Gas phase LIF study of the b\(^{1}\)\(\Sigma\)\(^{+}\)(b0\(^{+}\)) ↔ X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{1}\)0\(^{+}\),X\(_{2}\)1) transition of NI
Journal of Molecular Spectroscopy, 192 (1) :139-147
1998
Herausgeber: Academic Press778.
Shestakov, Oleg; Gielen, R.; Setzer, Klaus-Dieter; Fink, Ewald H.
Gas phase LIF study of the b1Σ+(b0+) ↔ X3Σ-(X10+,X21) transition of NI
Journal of Molecular Spectroscopy, 192 (1) :139-147
1998
Herausgeber: Academic Press777.
Adjiman, C.S.; Schweiger, C.A.; Floudas, C.A.
Handbook of Combinatorial Optimization
In Du, D.-Z. and Pardalos, P. M., Editor
Kapitel Mixed-Integer Nonlinear Optimization in Process Synthesis
Herausgeber: Kluwer Academic Publishers
1998776.
Kleffmann, Jörg; Becker, Karl Heinz; Wiesen, Peter
Heterogeneous NO\(_{2}\) conversion processes on acid surfaces
Atmospheric Environment, 32 (16) :2721-2729
1998775.
Kleffmann, Jörg; Becker, Karl Heinz; Wiesen, Peter
Heterogeneous NO\(_{2}\) conversion processes on acid surfaces
Atmospheric Environment, 32 (16) :2721-2729
1998774.
Kleffmann, Jörg; Becker, Karl Heinz; Wiesen, Peter
Heterogeneous NO2 conversion processes on acid surfaces
Atmospheric Environment, 32 (16) :2721-2729
1998773.
Ziebarth, K.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
High-resolution study of the X\(_{2}\) \(^{2}\)\(\Pi\)\(_{3/2}\) → X\(_{1}\) \(^{2}\)\(\Pi\)\(_{1/2}\) fine structure transitions of PbF and PbCl
Journal of Molecular Spectroscopy, 191 (1) :108-116
1998
Herausgeber: Academic Press772.
Ziebarth, K.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
High-resolution study of the X\(_{2}\) \(^{2}\)\(\Pi\)\(_{3/2}\) → X\(_{1}\) \(^{2}\)\(\Pi\)\(_{1/2}\) fine structure transitions of PbF and PbCl
Journal of Molecular Spectroscopy, 191 (1) :108-116
1998
Herausgeber: Academic Press771.
Ziebarth, K.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
High-resolution study of the X2 2Π3/2 → X1 2Π1/2 fine structure transitions of PbF and PbCl
Journal of Molecular Spectroscopy, 191 (1) :108-116
1998
Herausgeber: Academic Press770.
Kleffmann, Jörg; Becker, Karl Heinz; Wiesen, Peter
Investigation of the heterogeneous NO\(_{2}\) conversion on perchloric acid surfaces
Journal of the Chemical Society - Faraday Transactions, 94 (21) :3289-3292
1998
Herausgeber: Royal Society of Chemistry
