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
- 1997
677.
Schryber, Jeremy H.; Polyansky, Oleg L.; Jensen, Per; Tennyson, Jonathan
On the spectroscopically determined potential energy surfaces for the electronic ground states of NO\(_{2}\) and H\(_{2}\)O
Journal of Molecular Spectroscopy, 185 (2) :234-243
1997
Herausgeber: Academic Press676.
Schryber, Jeremy H.; Polyansky, Oleg L.; Jensen, Per; Tennyson, Jonathan
On the spectroscopically determined potential energy surfaces for the electronic ground states of NO\(_{2}\) and H\(_{2}\)O
Journal of Molecular Spectroscopy, 185 (2) :234-243
1997
Herausgeber: Academic Press675.
Ehrgott, Matthias; Klamroth, Kathrin
Nonconnected efficiency graphs in multiple criteria combinatorial optimization
In Caballero, R. and Ruiz, F. and Steuer, R.E., Editor, Advances in Multiple Objective and Goal ProgrammingBand455ausLecture Notes in Economics and Mathematical Systems, Seite 140-150
In Caballero, R. and Ruiz, F. and Steuer, R.E., Editor
1997674.
G\"unther, Michael
Modelling transmission lines effects in integrated circuits by a mixed system of {DAEs} and {PDEs}
In I.~Troch and F.~Breitenecker, Editor, 2nd MATHMOD Vienna. Proceedings IMACS Symposium on Mathematical ModellingBand11ausArgesim Report, Seite 535--540
In I.~Troch and F.~Breitenecker, Editor
Herausgeber: TU Wien
Februar 1997673.
Tausch, Michael W.; Brandl, H.
Lichtbeteiligung bei chemischen Reaktionen
MNU, 50 :206
1997672.
Klamroth, Kathrin; Mengersen, Ingrid
The Ramsey number r(K_1,3,C_4,K_4)
Utilitas Mathematica, 52 :65-81
1997671.
Becker, Karl Heinz; Kurtenbach, Ralf; Schmidt, Frank; Wiesen, Peter
Kinetics of the Reactions of NCO Radicals with NO and NH3
Berichte der Bunsengesellschaft für physikalische Chemie, 101 (1) :128-133
1997670.
Becker, Karl Heinz; Kurtenbach, Ralf; Schmidt, Frank; Wiesen, Peter
Kinetics of the Reactions of NCO Radicals with NO and NH\(_{3}\)
Berichte der Bunsengesellschaft für physikalische Chemie, 101 (1) :128-133
1997669.
Becker, Karl Heinz; Kurtenbach, Ralf; Schmidt, Frank; Wiesen, Peter
Kinetics of the Reactions of NCO Radicals with NO and NH\(_{3}\)
Berichte der Bunsengesellschaft für physikalische Chemie, 101 (1) :128-133
1997668.
Chance, K. V.; Park, K.; Evenson, K. M.; Zink, L. R.; Stroh, Fred; Fink, Ewald H.; Ramsay, D. A.
Improved Molecular Constants for the Ground State of HO2
Journal of Molecular Spectroscopy, 183 (2) :418
1997
Herausgeber: Academic Press667.
Chance, K. V.; Park, K.; Evenson, K. M.; Zink, L. R.; Stroh, Fred; Fink, Ewald H.; Ramsay, D. A.
Improved Molecular Constants for the Ground State of HO\(_{2}\)
Journal of Molecular Spectroscopy, 183 (2) :418
1997
Herausgeber: Academic Press666.
Chance, K. V.; Park, K.; Evenson, K. M.; Zink, L. R.; Stroh, Fred; Fink, Ewald H.; Ramsay, D. A.
Improved Molecular Constants for the Ground State of HO\(_{2}\)
Journal of Molecular Spectroscopy, 183 (2) :418
1997
Herausgeber: Academic Press665.
Schindler, Ralph N.; Liesner, M.; Schmidt, Sven; Kirchner, Ulf; Benter, Thorsten
Identification of nascent products formed in the laser photolysis of CH3OCl and HOCl at 308 nm and around 235 nm. Total Cl-atom quantum yields and the state and velocity distributions of Cl(2Pj)
Journal of Photochemistry and Photobiology A: Chemistry, 107 (1-3) :9-19
1997664.
Schindler, Ralph N.; Liesner, M.; Schmidt, Sven; Kirchner, Ulf; Benter, Thorsten
Identification of nascent products formed in the laser photolysis of CH\(_{3}\)OCl and HOCl at 308 nm and around 235 nm. Total Cl-atom quantum yields and the state and velocity distributions of Cl(\(^{2}\)P\(_{j}\))
Journal of Photochemistry and Photobiology A: Chemistry, 107 (1-3) :9-19
1997663.
Schindler, Ralph N.; Liesner, M.; Schmidt, Sven; Kirchner, Ulf; Benter, Thorsten
Identification of nascent products formed in the laser photolysis of CH\(_{3}\)OCl and HOCl at 308 nm and around 235 nm. Total Cl-atom quantum yields and the state and velocity distributions of Cl(\(^{2}\)P\(_{j}\))
Journal of Photochemistry and Photobiology A: Chemistry, 107 (1-3) :9-19
1997662.
Fink, Ewald H.; Ramsay, D. A.
High-resolution study of the A~ 2A' → X~ 2A" transition of HO2: Analysis of the 000-000 band
Journal of Molecular Spectroscopy, 185 (2) :304-324
1997
Herausgeber: Academic Press661.
Fink, Ewald H.; Ramsay, D. A.
High-resolution study of the A\verb=~= \(^{2}\)A' → X\verb=~= \(^{2}\)A'' transition of HO\(_{2}\): Analysis of the 000-000 band
Journal of Molecular Spectroscopy, 185 (2) :304-324
1997
Herausgeber: Academic Press660.
Fink, Ewald H.; Ramsay, D. A.
High-resolution study of the A\verb=~= \(^{2}\)A' → X\verb=~= \(^{2}\)A'' transition of HO\(_{2}\): Analysis of the 000-000 band
Journal of Molecular Spectroscopy, 185 (2) :304-324
1997
Herausgeber: Academic Press659.
Kozin, Igor N.; Jensen, Per
The Effects of Nonzero Total Electron Spin in the X~ 3B1 State of Methylene CH2
Journal of Molecular Spectroscopy, 183 (2) :398-406
1997
Herausgeber: Academic Press- 1996
658.
Arste, J.; Klamroth, Kathrin; Mengersen, Ingrid
Three color Ramsey numbers for small graphs
Utilitas Mathematica, 49 :85--96
1996657.
[german] Tausch, Michael W.
Ungleiche Gleichgewichte
{CHEMKON}, 3 (3) :123--127
1996
Herausgeber: Wiley656.
Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a1Δ(a2) States of BiCl, BiBr, and BiI
Journal of Molecular Spectroscopy, 175 (1) :48-53
1996
Herausgeber: Academic Press655.
Bunker, Philip R.; Jensen, Per; Yamaguchi, Yukio; Schaefer III, Henry F.
The Rovibrational Energy Levels of Quasilinear c~ 1A1 Methylene
Journal of Molecular Spectroscopy, 179 (2) :263-268
1996
Herausgeber: Academic Press654.
Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\)(a2) States of BiCl, BiBr, and BiI
Journal of Molecular Spectroscopy, 175 (1) :48-53
1996
Herausgeber: Academic Press653.
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
1996
