Applied and Computational Mathematics (ACM)

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

1992

405.

Tausch, Michael W.; Wachtendonk, M.; Deissenberger, H.; Porth, H.-R.; Weißenhorn, R.G.
STOFF-FORMEL-UMWELT, BAND 2: ORGANISCHE CHEMIE - ANGEWANDTE CHEMIE, Lehrbuch für die S II, (Grund- und Leistungskurse), 272 Seiten
Herausgeber: C. C. Buchner, Bamberg
1992

404.

Becker, Karl Heinz; Engelhardt, B.; Geiger, Harald; Kurtenbach, Ralf; Schrey, G.; Wiesen, Peter
Temperature dependence of the CH+N\(_{2}\) reaction at low total pressure
Chemical Physics Letters, 195 (4) :322-328
1992

DOI: 10.1016/0009-2614(92)85610-M

403.

Becker, Karl Heinz; Engelhardt, B.; Geiger, Harald; Kurtenbach, Ralf; Schrey, G.; Wiesen, Peter
Temperature dependence of the CH+N\(_{2}\) reaction at low total pressure
Chemical Physics Letters, 195 (4) :322-328
1992

DOI: 10.1016/0009-2614(92)85610-M

402.

Benter, Thorsten; Becker, Eilhard; Wille, Uta; Rahman, M. M.; Schindler, Ralph N.
The Determination of Rate Constants for the Reactions of Some Alkenes with the NO\(_{3}\) Radical
Berichte der Bunsengesellschaft für physikalische Chemie, 96 (6) :769-775
1992

DOI: 10.1002/bbpc.19920960607

401.

Tausch, Michael W.; Wachtendonk, M.; Deissenberger, H.; Porth, H.-R.; Weißenhorn, R.G.
Lehrerband mit didaktischen Hinweisen und Lösungen der Aufgaben zu STOFF-FORMEL-UMWELT, BAND 2: ORGANISCHE CHEMIE - ANGEWANDTE CHEMIE, Lehrbuch für die S II, (Grund- und Leistungskurse)
Herausgeber: C. C. Buchner, Bamberg
1992

400.

Benter, Thorsten; Becker, Eilhard; Wille, Uta; Rahman, M. M.; Schindler, Ralph N.
The Determination of Rate Constants for the Reactions of Some Alkenes with the NO\(_{3}\) Radical
Berichte der Bunsengesellschaft für physikalische Chemie, 96 (6) :769-775
1992

DOI: 10.1002/bbpc.19920960607

399.

Benter, Thorsten; Becker, Eilhard; Wille, Uta; Rahman, M. M.; Schindler, Ralph N.
The Determination of Rate Constants for the Reactions of Some Alkenes with the NO3 Radical
Berichte der Bunsengesellschaft für physikalische Chemie, 96 (6) :769-775
1992

DOI: 10.1002/bbpc.19920960607

398.

Ziebarth, K.; Breidohr, R.; Shestakov, Oleg; Fink, Ewald H.
The X\(_{2}\) \(^{2}\)\(\Pi\)\(_{3/2}\) → X\(_{1}\) \(^{2}\)\(\Pi\)\(_{1/2}\) electronic band systems of lead monohalides in the near infrared
Chemical Physics Letters, 190 (3-4) :271-278
1992

DOI: 10.1016/0009-2614(92)85338-B

397.

Ziebarth, K.; Breidohr, R.; Shestakov, Oleg; Fink, Ewald H.
The X\(_{2}\) \(^{2}\)\(\Pi\)\(_{3/2}\) → X\(_{1}\) \(^{2}\)\(\Pi\)\(_{1/2}\) electronic band systems of lead monohalides in the near infrared
Chemical Physics Letters, 190 (3-4) :271-278
1992

DOI: 10.1016/0009-2614(92)85338-B

396.

Ziebarth, K.; Breidohr, R.; Shestakov, Oleg; Fink, Ewald H.
The X2 2Π3/2 → X1 2Π1/2 electronic band systems of lead monohalides in the near infrared
Chemical Physics Letters, 190 (3-4) :271-278
1992

DOI: 10.1016/0009-2614(92)85338-B

395.

Barone, Vincenzo; Jensen, Per; Minichino, Camilla
Vibro-rotational analysis of Si\(_{2}\)C from an ab initio potential energy surface. A comparison between perturbative and variational methods
Journal of Molecular Spectroscopy, 154 (2) :252-264
1992

DOI: 10.1016/0022-2852(92)90206-4

394.

Barone, Vincenzo; Jensen, Per; Minichino, Camilla
Vibro-rotational analysis of Si\(_{2}\)C from an ab initio potential energy surface. A comparison between perturbative and variational methods
Journal of Molecular Spectroscopy, 154 (2) :252-264
1992

DOI: 10.1016/0022-2852(92)90206-4

393.

Barone, Vincenzo; Jensen, Per; Minichino, Camilla
Vibro-rotational analysis of Si2C from an ab initio potential energy surface. A comparison between perturbative and variational methods
Journal of Molecular Spectroscopy, 154 (2) :252-264
1992

DOI: 10.1016/0022-2852(92)90206-4

392.

Shestakov, Oleg; Pravilov, A. M.; Demes, H.; Fink, Ewald H.
Radiative lifetime and quenching of the A \(^{2}\)\(\Sigma\)\(^{+}\) and X\(_{2}\) \(^{2}\)\(\Pi\)\(_{3/2}\) states of PbF
Chemical Physics, 165 (2-3) :415-427
1992

DOI: 10.1016/0301-0104(92)87056-F

391.

G\"unther, Michael
Multirate {Rosenbrock}-{Wanner} Verfahren zur Integration von elektrischen Schaltkreisen
Technische Universit\"at at M\"unchen
1992

390.

Becker, Karl Heinz; König, R.; Meuser, R.; Wiesen, Peter; Bayes, Kyle D.
Kinetics of C2O radicals formed in the photolysis of carbon suboxide at 308 and 248 nm
Journal of Photochemistry and Photobiology, A: Chemistry, 64 (1) :1-14
1992

DOI: 10.1016/1010-6030(92)85089-D

389.

Jensen, Per; Rohlfing, Celeste Michael; Almlöf, Jan
Calculation of the complete-active-space self-consistent-field potential-energy surface, the dipole moment surfaces, the rotation-vibration energies, and the vibrational transition moments for C3(X~ 1Σg+)
The Journal of Chemical Physics, 97 (5) :3399-3411
1992

DOI: 10.1063/1.462976

388.

Kraemer, Wolfgang P.; Jensen, Per; Roos, B. O.; Bunker, Philip R.
Ab initio rotation-vibration energies and intensities for the HNC\(^{+}\) molecule
Journal of Molecular Spectroscopy, 153 (1-2) :240-254
1992

DOI: 10.1016/0022-2852(92)90472-Z

387.

Kraemer, Wolfgang P.; Jensen, Per; Roos, B. O.; Bunker, Philip R.
Ab initio rotation-vibration energies and intensities for the HNC\(^{+}\) molecule
Journal of Molecular Spectroscopy, 153 (1-2) :240-254
1992

DOI: 10.1016/0022-2852(92)90472-Z

386.

Kraemer, Wolfgang P.; Jensen, Per; Roos, B. O.; Bunker, Philip R.
Ab initio rotation-vibration energies and intensities for the HNC+ molecule
Journal of Molecular Spectroscopy, 153 (1-2) :240-254
1992

DOI: 10.1016/0022-2852(92)90472-Z

385.

Jensen, Per; Bunker, Philip R.; Epa, V. C.; Karpfen, Alfred
An ab initio calculation of the fundamental and overtone HCl stretching vibrations for the HCl dimer
Journal of Molecular Spectroscopy, 151 (2) :384-395
1992

DOI: 10.1016/0022-2852(92)90574-8

384.

Jensen, Per; Bunker, Philip R.; Epa, V. C.; Karpfen, Alfred
An ab initio calculation of the fundamental and overtone HCl stretching vibrations for the HCl dimer
Journal of Molecular Spectroscopy, 151 (2) :384-395
1992

DOI: 10.1016/0022-2852(92)90574-8

383.

Jensen, Per; Bunker, Philip R.; Epa, V. C.; Karpfen, Alfred
An ab initio calculation of the fundamental and overtone HCl stretching vibrations for the HCl dimer
Journal of Molecular Spectroscopy, 151 (2) :384-395
1992

DOI: 10.1016/0022-2852(92)90574-8

382.

Jensen, Per; Rohlfing, Celeste Michael; Alml{ö}f, Jan
Calculation of the complete-active-space self-consistent-field potential-energy surface, the dipole moment surfaces, the rotation-vibration energies, and the vibrational transition moments for C\(_{3}\)(X\verb=~= \(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\))
The Journal of Chemical Physics, 97 (5) :3399-3411
1992

DOI: 10.1063/1.462976

381.

Jensen, Per; Rohlfing, Celeste Michael; Alml{ö}f, Jan
Calculation of the complete-active-space self-consistent-field potential-energy surface, the dipole moment surfaces, the rotation-vibration energies, and the vibrational transition moments for C\(_{3}\)(X\verb=~= \(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\))
The Journal of Chemical Physics, 97 (5) :3399-3411
1992

DOI: 10.1063/1.462976

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