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
325.
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
1991317.
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
1991316.
Jensen, Per; Paidarov{{\'a}}, Ivana; Vojt{í}k, Jan; Spirko, Vladim{í}r
Theoretical calculations of the nuclear quadrupole coupling in the spectra of D\(_{3}\)\(^{+}\), H\(_{2}\)D\(^{+}\), and HD\(_{2}\)\(^{+}\)
Journal of Molecular Spectroscopy, 150 (1) :137-163
1991315.
Jensen, Per; Paidarov{{\'a}}, Ivana; Vojt{í}k, Jan; Spirko, Vladim{í}r
Theoretical calculations of the nuclear quadrupole coupling in the spectra of D\(_{3}\)\(^{+}\), H\(_{2}\)D\(^{+}\), and HD\(_{2}\)\(^{+}\)
Journal of Molecular Spectroscopy, 150 (1) :137-163
1991314.
Jensen, Per; Paidarová, Ivana; Vojtík, Jan; Spirko, Vladimír
Theoretical calculations of the nuclear quadrupole coupling in the spectra of D3+, H2D+, and HD2+
Journal of Molecular Spectroscopy, 150 (1) :137-163
1991313.
[german] Tausch, Michael W.; Mundt, C.; Kehlenbeck, V.
Vollständige Mineralisierung von Perchlorethylen PER
Praxis der Naturwissenschaften (Chemie), 40 :28
1991- 1990
312.
Tausch, Michael W.; Kühn, S.
''Chemische Gleichgewichte - Elektrochemie'' - Diskette mit Programmen zu STOFF UND FORMEL II, Lehrbuch für die S II (Grundkurse)
Herausgeber: C. C. Buchner, Bamberg
1990311.
Bunker, Philip R.; Jensen, Per; Wright, J. S.; Hamilton, I. P.
Ab initio rotation-vibration energies and intensities for the H\(_{2}\)F\(^{+}\) molecule
Journal of Molecular Spectroscopy, 144 (2) :310-322
1990310.
Bunker, Philip R.; Jensen, Per; Wright, J. S.; Hamilton, I. P.
Ab initio rotation-vibration energies and intensities for the H\(_{2}\)F\(^{+}\) molecule
Journal of Molecular Spectroscopy, 144 (2) :310-322
1990309.
Bunker, Philip R.; Jensen, Per; Wright, J. S.; Hamilton, I. P.
Ab initio rotation-vibration energies and intensities for the H2F+ molecule
Journal of Molecular Spectroscopy, 144 (2) :310-322
1990308.
Jensen, Per; Bunker, Philip R.; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the intramolecular stretching spectra for the HF dimer and its D-substituted isotopic species
The Journal of Chemical Physics, 93 (9) :6266-6280
1990307.
Jensen, Per; Bunker, Philip R.; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the intramolecular stretching spectra for the HF dimer and its D-substituted isotopic species
The Journal of Chemical Physics, 93 (9) :6266-6280
1990306.
Jensen, Per; Bunker, Philip R.; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the intramolecular stretching spectra for the HF dimer and its D-substituted isotopic species
The Journal of Chemical Physics, 93 (9) :6266-6280
1990305.
Jensen, Per; Buenker, Robert J.; Hirsch, Gerhard; Rai, Sachchida N.
An ab initio calculation of the rotational-vibrational energies in the electronic ground state of NH\(_{2}\)
Molecular Physics, 70 (3) :443-454
1990304.
Jensen, Per; Buenker, Robert J.; Hirsch, Gerhard; Rai, Sachchida N.
An ab initio calculation of the rotational-vibrational energies in the electronic ground state of NH\(_{2}\)
Molecular Physics, 70 (3) :443-454
1990303.
Jensen, Per; Buenker, Robert J.; Hirsch, Gerhard; Rai, Sachchida N.
An ab initio calculation of the rotational-vibrational energies in the electronic ground state of NH2
Molecular Physics, 70 (3) :443-454
1990302.
Bunker, Philip R.; Jensen, Per; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the stretching energies for the HF dimer
The Journal of Chemical Physics, 92 (12) :7432-7440
1990301.
Bunker, Philip R.; Jensen, Per; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the stretching energies for the HF dimer
The Journal of Chemical Physics, 92 (12) :7432-7440
1990
