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
352.
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
1991351.
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
1991350.
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
1991349.
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
1991348.
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
1991347.
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
1991346.
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
1991345.
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
1991344.
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
1991343.
Vilesov, A. F.; Wildt, Jürgen; Fink, Ewald H.
Emission of Xe: N(2P) collision complexes near the N(2P→2D) lines
Chemical Physics, 153 (3) :531-537
1991342.
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
1991341.
Vilesov, A. F.; Wildt, J{ü}rgen; Fink, Ewald H.
Emission of Xe: N(\(^{2}\)P) collision complexes near the N(\(^{2}\)P→\(^{2}\)D) lines
Chemical Physics, 153 (3) :531-537
1991340.
Vilesov, A. F.; Wildt, J{ü}rgen; Fink, Ewald H.
Emission of Xe: N(\(^{2}\)P) collision complexes near the N(\(^{2}\)P→\(^{2}\)D) lines
Chemical Physics, 153 (3) :531-537
1991339.
Fink, Ewald H.; Setzer, Klaus-Dieter; Wildt, Jürgen; Ramsay, D. A.; Vervloet, M.
Collision-induced emission of O2(b1Σg+ → a1Δg) in the gas phase
International Journal of Quantum Chemistry, 39 (3) :287-298
1991338.
Fink, Ewald H.; Setzer, Klaus-Dieter; Wildt, J{ü}rgen; Ramsay, D. A.; Vervloet, M.
Collision-induced emission of O\(_{2}\)(b\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → a\(^{1}\)\(\Delta\)\(_{g}\)) in the gas phase
International Journal of Quantum Chemistry, 39 (3) :287-298
1991337.
Fink, Ewald H.; Setzer, Klaus-Dieter; Wildt, J{ü}rgen; Ramsay, D. A.; Vervloet, M.
Collision-induced emission of O\(_{2}\)(b\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → a\(^{1}\)\(\Delta\)\(_{g}\)) in the gas phase
International Journal of Quantum Chemistry, 39 (3) :287-298
1991336.
Bunker, Philip R.; Epa, V. C.; Jensen, Per; Karpfen, Alfred
An analytical ab initio potential surface and the calculated tunneling energies for the HCl dimer
Journal of Molecular Spectroscopy, 146 (1) :200-219
1991335.
Bunker, Philip R.; Epa, V. C.; Jensen, Per; Karpfen, Alfred
An analytical ab initio potential surface and the calculated tunneling energies for the HCl dimer
Journal of Molecular Spectroscopy, 146 (1) :200-219
1991334.
Bunker, Philip R.; Epa, V. C.; Jensen, Per; Karpfen, Alfred
An analytical ab initio potential surface and the calculated tunneling energies for the HCl dimer
Journal of Molecular Spectroscopy, 146 (1) :200-219
1991333.
Karpfen, Alfred; Bunker, Philip R.; Jensen, Per
An ab initio study of the hydrogen chloride dimer: the potential energy surface and the characterization of the stationary points
Chemical Physics, 149 (3) :299-309
1991332.
Karpfen, Alfred; Bunker, Philip R.; Jensen, Per
An ab initio study of the hydrogen chloride dimer: the potential energy surface and the characterization of the stationary points
Chemical Physics, 149 (3) :299-309
1991331.
Karpfen, Alfred; Bunker, Philip R.; Jensen, Per
An ab initio study of the hydrogen chloride dimer: the potential energy surface and the characterization of the stationary points
Chemical Physics, 149 (3) :299-309
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.
Bunker, Philip R.; Jensen, Per; Karpfen, Alfred
The ν1 + ν2 = 4 stretching overtones of the HF dimer, and H-atom exchange
Journal of Molecular Spectroscopy, 149 (2) :512-518
1991
