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
- 1991
342.
Jensen, Per; Oddershede, Jens; Sabin, John R.
Geometric dependence of the mean excitation energy and spectral moments of water
Physical Review A, 43 (7) :4040-4043
1991341.
Jensen, Per; Oddershede, Jens; Sabin, John R.
Geometric dependence of the mean excitation energy and spectral moments of water
Physical Review A, 43 (7) :4040-4043
1991340.
Jensen, Per; Oddershede, Jens; Sabin, John R.
Geometric dependence of the mean excitation energy and spectral moments of water
Physical Review A, 43 (7) :4040-4043
1991339.
Becker, Karl Heinz; Geiger, Harald; Wiesen, Peter
Kinetic study of the OH radical chain in the reaction system OH + C\(_{2}\)H\(_{4}\) + NO + air
Chemical Physics Letters, 184 (4) :256-261
1991338.
Becker, Karl Heinz; Geiger, Harald; Wiesen, Peter
Kinetic study of the OH radical chain in the reaction system OH + C\(_{2}\)H\(_{4}\) + NO + air
Chemical Physics Letters, 184 (4) :256-261
1991337.
Becker, Karl Heinz; Geiger, Harald; Wiesen, Peter
Kinetic study of the OH radical chain in the reaction system OH + C2H4 + NO + air
Chemical Physics Letters, 184 (4) :256-261
1991336.
Wildt, J{ü}rgen; Bednarek, G.; Fink, Ewald H.; Wayne, Richard P.
Laser excitation of the A\(^{3}\)\(\Sigma\)\(_{u}\)\(^{+}\), A'\(^{3}\)\(\Delta\)\(_{u}\) and c\(^{1}\)\(\Sigma\)\(_{u}\)\(^{-}\) states of molecular oxygen
Chemical Physics, 156 (3) :497-508
1991335.
Wildt, J{ü}rgen; Bednarek, G.; Fink, Ewald H.; Wayne, Richard P.
Laser excitation of the A\(^{3}\)\(\Sigma\)\(_{u}\)\(^{+}\), A'\(^{3}\)\(\Delta\)\(_{u}\) and c\(^{1}\)\(\Sigma\)\(_{u}\)\(^{-}\) states of molecular oxygen
Chemical Physics, 156 (3) :497-508
1991334.
Wildt, Jürgen; Bednarek, G.; Fink, Ewald H.; Wayne, Richard P.
Laser excitation of the A3Σu+, A'3Δu and c1Σu- states of molecular oxygen
Chemical Physics, 156 (3) :497-508
1991333.
Tausch, Michael W.
Legende oder nicht Legende?
Praxis der Naturwissenschaften (Chemie), 40 :44
1991332.
Benter, Thorsten; Becker, Eilhard; Wille, Uta; Schindler, Ralph N.; Canosa-Mas, Carlos E.; Smith, Stuart J.; Waygood, Steven J.; Wayne, Richard P.
Nitrate radical reactions: interactions with alkynes
Journal of the Chemical Society, Faraday Transactions, 87 (14) :2141
1991331.
Benter, Thorsten; Becker, Eilhard; Wille, Uta; Schindler, Ralph N.; Canosa-Mas, Carlos E.; Smith, Stuart J.; Waygood, Steven J.; Wayne, Richard P.
Nitrate radical reactions: interactions with alkynes
Journal of the Chemical Society, Faraday Transactions, 87 (14) :2141
1991330.
Benter, Thorsten; Becker, Eilhard; Wille, Uta; Schindler, Ralph N.; Canosa-Mas, Carlos E.; Smith, Stuart J.; Waygood, Steven J.; Wayne, Richard P.
Nitrate radical reactions: interactions with alkynes
Journal of the Chemical Society, Faraday Transactions, 87 (14) :2141
1991329.
[german] Tausch, Michael W.
Photochemie - aktuelle Bedeutung und Möglichkeiten der Integration in den Chemieunterricht
Praxis der Naturwissenschaften (Chemie), 40 (4) :2
1991328.
Becker, Karl Heinz; Kurtenbach, Ralf; Wiesen, Peter
Temperature and pressure dependence of the reaction methylidyne radical + hydrogen
The Journal of Physical Chemistry, 95 (6) :2390-2394
1991327.
Becker, Karl Heinz; Kurtenbach, Ralf; Wiesen, Peter
Temperature and pressure dependence of the reaction methylidyne radical + hydrogen
The Journal of Physical Chemistry, 95 (6) :2390-2394
1991326.
Becker, Karl Heinz; Kurtenbach, Ralf; Wiesen, Peter
Temperature and pressure dependence of the reaction methylidyne radical + hydrogen
The Journal of Physical Chemistry, 95 (6) :2390-2394
1991325.
Bunker, Philip R.; Jensen, Per; Karpfen, Alfred
The \(\nu\)\(_{1}\) + \(\nu\)\(_{2}\) = 4 stretching overtones of the HF dimer, and H-atom exchange
Journal of Molecular Spectroscopy, 149 (2) :512-518
1991324.
Bunker, Philip R.; Jensen, Per; Karpfen, Alfred
The \(\nu\)\(_{1}\) + \(\nu\)\(_{2}\) = 4 stretching overtones of the HF dimer, and H-atom exchange
Journal of Molecular Spectroscopy, 149 (2) :512-518
1991323.
Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
The X\(_{2}\)\(^{2}\)\(\Pi\)\(_{1/2}\) → X\(_{1}\)\(^{2}\)\(\Pi\)\(_{3/2}\) electronic transitions of tellurium monohalides in the near infrared
Chemical Physics Letters, 177 (3) :265-268
1991322.
Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
The X\(_{2}\)\(^{2}\)\(\Pi\)\(_{1/2}\) → X\(_{1}\)\(^{2}\)\(\Pi\)\(_{3/2}\) electronic transitions of tellurium monohalides in the near infrared
Chemical Physics Letters, 177 (3) :265-268
1991321.
Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
The X\(_{2}\)1 → X\(_{1}\)0\(^{+}\) electronic band systems of bismuth monohalides in the near infrared
Chemical Physics Letters, 179 (1-2) :95-102
1991320.
Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
The X\(_{2}\)1 → X\(_{1}\)0\(^{+}\) electronic band systems of bismuth monohalides in the near infrared
Chemical Physics Letters, 179 (1-2) :95-102
1991319.
Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
The X22Π1/2 → X12Π3/2 electronic transitions of tellurium monohalides in the near infrared
Chemical Physics Letters, 177 (3) :265-268
1991318.
Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
The X21 → X10+ electronic band systems of bismuth monohalides in the near infrared
Chemical Physics Letters, 179 (1-2) :95-102
1991
