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: 403.
Wildt, J{ü}rgen; Fink, Ewald H.; Biggs, P.; Wayne, Richard P.; Vilesov, A. F.
Collision-induced emission of O\(_{2}\)(a \(^{1}\)\(\Delta\)\(_{g}\) → X \(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\)) in the gas phase
Chemical Physics, 159 (1) :127-140
1992
DOI: 10.1016/0301-0104(92)80065-4; 402.
Wildt, J{ü}rgen; Fink, Ewald H.; Biggs, P.; Wayne, Richard P.; Vilesov, A. F.
Collision-induced emission of O\(_{2}\)(a \(^{1}\)\(\Delta\)\(_{g}\) → X \(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\)) in the gas phase
Chemical Physics, 159 (1) :127-140
1992
DOI: 10.1016/0301-0104(92)80065-4; 401.
Wildt, Jürgen; Fink, Ewald H.; Biggs, P.; Wayne, Richard P.; Vilesov, A. F.
Collision-induced emission of O2(a 1Δg → X 3Σg-) in the gas phase
Chemical Physics, 159 (1) :127-140
1992
DOI: 10.1016/0301-0104(92)80065-4; 400.
Heilmann, Margareta
Erhöhung der Konvergenzgeschwindigkeit bei der Approximation von Funktionen mit Hilfe von Linearkombinationen spezieller positiver linearer Operatoren
Universität Dortmund
1992
Download; 399.
Tausch, Michael W.
Erzeugung und Desaktivierung von angeregten Zuständen
Mitteilungsblatt der FG Chemieunterricht der GDCh (17) :253
1992; 398.
Becker, Karl Heinz; Kurtenbach, Ralf; Wiesen, Peter
Investigation of N\(_{2}\)O formation in the NCO+NO reaction by Fourier-transform infrared spectroscopy
Chemical Physics Letters, 198 (3-4) :424-428
1992
DOI: 10.1016/0009-2614(92)85076-M; 397.
Becker, Karl Heinz; Kurtenbach, Ralf; Wiesen, Peter
Investigation of N\(_{2}\)O formation in the NCO+NO reaction by Fourier-transform infrared spectroscopy
Chemical Physics Letters, 198 (3-4) :424-428
1992
DOI: 10.1016/0009-2614(92)85076-M; 396.
Becker, Karl Heinz; Kurtenbach, Ralf; Wiesen, Peter
Investigation of N2O formation in the NCO+NO reaction by Fourier-transform infrared spectroscopy
Chemical Physics Letters, 198 (3-4) :424-428
1992
DOI: 10.1016/0009-2614(92)85076-M; 395.
Becker, Karl Heinz; K{ö}nig, R.; Meuser, R.; Wiesen, Peter; Bayes, Kyle D.
Kinetics of C\(_{2}\)O 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; 394.
Becker, Karl Heinz; K{ö}nig, R.; Meuser, R.; Wiesen, Peter; Bayes, Kyle D.
Kinetics of C\(_{2}\)O 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; 393.
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; 392.
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; 391.
G\"unther, Michael
Multirate {Rosenbrock}-{Wanner} Verfahren zur Integration von elektrischen Schaltkreisen
Technische Universit\"at at M\"unchen
1992; 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 \(^{2}\)\(\Sigma\)\(^{+}\) 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; 388.
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; 387.
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; 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 HO\(_{2}\) molecule
Journal of Molecular Spectroscopy, 155 (1) :44-54
1992
DOI: 10.1016/0022-2852(92)90547-2; 384.
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; 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

Index Analysis

Group members working on that field

Cooperations

Publications

403.

402.

401.

400.

399.

398.

397.

396.

395.

394.

393.

392.

391.

390.

389.

388.

387.

386.

385.

384.

383.

382.

381.

380.

379.