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

392.

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

391.

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

390.

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

389.

Shestakov, Oleg; Pravilov, A. M.; Demes, H.; Fink, Ewald H.
Radiative lifetime and quenching of the A 2Σ+ and X2 2Π3/2 states of PbF
Chemical Physics, 165 (2-3) :415-427
1992

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

388.

Heilmann, Margareta
Rate of approximation of weighted derivatives by linear combinations of SMD-operators
Numerical Methods in Approximation Theory - Proceedings of the conference held in Oberwolfach Germany, November 24-30, 1991, Seite 97-115
In D. Braess et al., Editor
Herausgeber: Birkhäuser, Basel, Int. Ser. Numer. Math. 105
1992

DOI: 10.1007/978-3-0348-8619-2_6

387.

Bunker, Philip R.; Hamilton, I. P.; Jensen, Per
Rotation-vibration energies for the HO\(_{2}\) molecule
Journal of Molecular Spectroscopy, 155 (1) :44-54
1992

DOI: 10.1016/0022-2852(92)90547-2

386.

Bunker, Philip R.; Hamilton, I. P.; Jensen, Per
Rotation-vibration energies for the HO\(_{2}\) molecule
Journal of Molecular Spectroscopy, 155 (1) :44-54
1992

DOI: 10.1016/0022-2852(92)90547-2

385.

Bunker, Philip R.; Hamilton, I. P.; Jensen, Per
Rotation-vibration energies for the HO2 molecule
Journal of Molecular Spectroscopy, 155 (1) :44-54
1992

DOI: 10.1016/0022-2852(92)90547-2

384.

Maten, E. J. W.; Melissen, J. B. M.
Simulation of inductive heating
{IEEE} Transactions on Magnetics, 28 (2) :1287--1290
März 1992
Herausgeber: Institute of Electrical and Electronics Engineers ({IEEE})

DOI: 10.1109/20.123925

383.

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

382.

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

381.

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

380.

Becker, Karl Heinz; Engelhardt, B.; Geiger, Harald; Kurtenbach, Ralf; Schrey, G.; Wiesen, Peter
Temperature dependence of the CH+N2 reaction at low total pressure
Chemical Physics Letters, 195 (4) :322-328
1992

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

379.

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

378.

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

377.

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

376.

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

375.

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

374.

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

373.

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

372.

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

371.

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

1991

370.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
A new band spectrum of BiO in the near-infrared region
Chemical Physics Letters, 179 (1-2) :103-108
1991

DOI: 10.1016/0009-2614(91)90298-N

369.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
A new band spectrum of BiO in the near-infrared region
Chemical Physics Letters, 179 (1-2) :103-108
1991

DOI: 10.1016/0009-2614(91)90298-N

368.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
A new band spectrum of BiO in the near-infrared region
Chemical Physics Letters, 179 (1-2) :103-108
1991

DOI: 10.1016/0009-2614(91)90298-N