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
717.
Gómez, P. C.; Pacios, L. F.; Jensen, Per
Fourfold Clusters of Rovibrational Energies in H2Po Studied with an ab Initio Potential Energy Function
Journal of Molecular Spectroscopy, 186 (1) :99-104
1997
Herausgeber: Academic Press716.
Schindler, J. G.; Schindler, M. M.; Herna, K.; Kling, H.-W.
Glutardialdehyde and formaldehyde biosensors
Biomed. Tech. (Berl), 42 (9) :264
1997715.
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 Press714.
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 Press713.
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 Press712.
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
1997711.
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
1997710.
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
1997709.
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 Press708.
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 Press707.
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 Press706.
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
1997705.
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
1997704.
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
1997703.
Tausch, Michael W.; Brandl, H.
Lichtbeteiligung bei chemischen Reaktionen
MNU, 50 :206
1997702.
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 1997701.
Günther, Michael
Modelling transmission lines effects in integrated circuits by a mixed system of DAEs and PDEs
In Troch, I. and Breitenecker, F., Editor, 2nd MATHMOD Vienna. Proceedings IMACS Symposium on Mathematical ModellingBand11ausArgesim Report 15, Seite 535–540
In Troch, I. and Breitenecker, F., Editor
Herausgeber: TU Wien
1997700.
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
1997699.
Günther, Michael; Ostermann, Alexander
Numerical treatment of ordinary and algebra-differential equations
Preprint (1934)
1997
Herausgeber: Technische Hochschule Darmstadt698.
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 Press697.
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 Press696.
Schryber, Jeremy H.; Polyansky, Oleg L.; Jensen, Per; Tennyson, Jonathan
On the spectroscopically determined potential energy surfaces for the electronic ground states of NO2 and H2O
Journal of Molecular Spectroscopy, 185 (2) :234-243
1997
Herausgeber: Academic Press695.
Günther, M.; Hoschek, M.
ROW methods adapted to electric circuit simulation packages
Journal of Computational and Applied Mathematics, 82 (1) :159–170
1997
Herausgeber: Elsevier694.
Günther, Michael; Hoschek, Markus
ROW methods adapted to electric circuit simulation packages
Journal of computational and applied mathematics, 82 (1-2) :159--170
1997
Herausgeber: North-Holland693.
Tausch, Michael W.
Simulation von chemischen Gleichgewichten
Computer + Unterricht, 26 :35
1997
