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: 728.
Spirko, Vladimír; Mengel, Markus; Jensen, Per
Calculation of Rotation-Vibration Energy Levels in Ground State C3 by a Born-Oppenheimer-Type Separation of the Vibrational Motions
Journal of Molecular Spectroscopy, 183 (1) :129-138
1997
Herausgeber: Academic Press
DOI: 10.1006/jmsp.1996.7257; 727.
Ehrgott, Matthias; Klamroth, Kathrin
Connectedness of efficient solutions in multiple criteria combinatorial optimization
European Journal of Operational Research, 97 :159-166
1997
DOI: 10.1016/S0377-2217(96)00116-6; 726.

Discrete transparent boundary conditions for parabolic equations
ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik, 77 (2) :543--544
1997
Herausgeber: Berlin, Akademie Verlag [etc.]; 725.
Ehrhardt, Matthias
Discrete transparent boundary conditions for parabolic equations
ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik, 77 (S2) :S543–S592
1997
Herausgeber: WILEY-VCH Verlag
DOI: 10.1002/zamm.19970771405; 724.
Kirchner, Ulf; Benter, Thorsten; Schindler, Ralph N.
Experimental verification of gas phase bromine enrichment in reactions of HOBr with sea salt doped ice surfaces
Berichte der Bunsengesellschaft für physikalische Chemie, 101 (6) :975-977
1997
DOI: 10.1002/bbpc.19971010614; 723.
Kirchner, Ulf; Benter, Thorsten; Schindler, Ralph N.
Experimental verification of gas phase bromine enrichment in reactions of HOBr with sea salt doped ice surfaces
Berichte der Bunsengesellschaft für physikalische Chemie, 101 (6) :975-977
1997
DOI: 10.1002/bbpc.19971010614; 722.
Kirchner, Ulf; Benter, Thorsten; Schindler, Ralph N.
Experimental verification of gas phase bromine enrichment in reactions of HOBr with sea salt doped ice surfaces
Berichte der Bunsengesellschaft für physikalische Chemie, 101 (6) :975-977
1997
DOI: 10.1002/bbpc.19971010614; 721.
Fink, Ewald H.; Shestakov, Oleg; Setzer, Klaus-Dieter
Fine Structure Transitions of BiOH in the Near-Infrared Region
Journal of Molecular Spectroscopy, 183 (1) :163-167
1997
Herausgeber: Academic Press
DOI: 10.1006/JMSP.1997.7262; 720.
Fink, Ewald H.; Shestakov, Oleg; Setzer, Klaus-Dieter
Fine Structure Transitions of BiOH in the Near-Infrared Region
Journal of Molecular Spectroscopy, 183 (1) :163-167
1997
Herausgeber: Academic Press
DOI: 10.1006/JMSP.1997.7262; 719.
Fink, Ewald H.; Shestakov, Oleg; Setzer, Klaus-Dieter
Fine Structure Transitions of BiOH in the Near-Infrared Region
Journal of Molecular Spectroscopy, 183 (1) :163-167
1997
Herausgeber: Academic Press
DOI: 10.1006/JMSP.1997.7262; 718.
G{{\'o}}mez, P. C.; Pacios, L. F.; Jensen, Per
Fourfold Clusters of Rovibrational Energies in H\(_{2}\)Po Studied with an ab Initio Potential Energy Function
Journal of Molecular Spectroscopy, 186 (1) :99-104
1997
Herausgeber: Academic Press
DOI: 10.1006/jmsp.1997.7434; 717.
G{{\'o}}mez, P. C.; Pacios, L. F.; Jensen, Per
Fourfold Clusters of Rovibrational Energies in H\(_{2}\)Po Studied with an ab Initio Potential Energy Function
Journal of Molecular Spectroscopy, 186 (1) :99-104
1997
Herausgeber: Academic Press
DOI: 10.1006/jmsp.1997.7434; 716.
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 Press
DOI: 10.1006/jmsp.1997.7434; 715.
Schindler, J. G.; Schindler, M. M.; Herna, K.; Kling, H.-W.
Glutardialdehyde and formaldehyde biosensors
Biomed. Tech. (Berl), 42 (9) :264
1997; 714.
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 Press
DOI: 10.1006/jmsp.1997.7401; 713.
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 Press
DOI: 10.1006/jmsp.1997.7401; 712.
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 Press
DOI: 10.1006/jmsp.1997.7401; 711.
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
1997
DOI: 10.1016/S1010-6030(96)04583-2; 710.
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
1997
DOI: 10.1016/S1010-6030(96)04583-2; 709.
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
1997
DOI: 10.1016/S1010-6030(96)04583-2; 708.
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 Press
DOI: 10.1006/JMSP.1997.7282; 707.
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 Press
DOI: 10.1006/JMSP.1997.7282; 706.
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 Press
DOI: 10.1006/JMSP.1997.7282; 705.
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
1997
DOI: 10.1002/bbpc.19971010117; 704.
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
1997
DOI: 10.1002/bbpc.19971010117

Index Analysis

Group members working on that field

Cooperations

Publications

728.

727.

726.

725.

724.

723.

722.

721.

720.

719.

718.

717.

716.

715.

714.

713.

712.

711.

710.

709.

708.

707.

706.

705.

704.