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: 380.
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; 379.
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; 378.
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; 377.
Heilmann, Margareta
Erhöhung der Konvergenzgeschwindigkeit bei der Approximation von Funktionen mit Hilfe von Linearkombinationen spezieller positiver linearer Operatoren
Universität Dortmund
1992
Download; 376.
Tausch, Michael W.
Erzeugung und Desaktivierung von angeregten Zuständen
Mitteilungsblatt der FG Chemieunterricht der GDCh (17) :253
1992; 375.
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; 374.
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; 373.
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; 372.
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; 371.
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
1991: 370.
Jensen, Per; Bunker, Philip R.; Karpfen, Alfred
An ab initio calculation of the nonadiabatic effect on the tunneling splitting in vibrationally excited (HF)\(_{2}\)
Journal of Molecular Spectroscopy, 148 (2) :385-390
1991
DOI: 10.1016/0022-2852(91)90395-Q; 369.
Jensen, Per; Marshall, Mark D.; Bunker, Philip R.; Karpfen, Alfred
An ab initio close-coupling calculation of the lower vibrational energies of the HCl dimer
Chemical Physics Letters, 180 (6) :594-600
1991
DOI: 10.1016/0009-2614(91)85016-P; 368.
Jensen, Per; Marshall, Mark D.; Bunker, Philip R.; Karpfen, Alfred
An ab initio close-coupling calculation of the lower vibrational energies of the HCl dimer
Chemical Physics Letters, 180 (6) :594-600
1991
DOI: 10.1016/0009-2614(91)85016-P; 367.
Jensen, Per; Bunker, Philip R.; Karpfen, Alfred
An ab initio calculation of the nonadiabatic effect on the tunneling splitting in vibrationally excited (HF)2
Journal of Molecular Spectroscopy, 148 (2) :385-390
1991
DOI: 10.1016/0022-2852(91)90395-Q; 366.
Jensen, Per; Bunker, Philip R.; Karpfen, Alfred
An ab initio calculation of the nonadiabatic effect on the tunneling splitting in vibrationally excited (HF)\(_{2}\)
Journal of Molecular Spectroscopy, 148 (2) :385-390
1991
DOI: 10.1016/0022-2852(91)90395-Q; 365.
Marshall, Mark D.; Jensen, Per; Bunker, Philip R.
An ab initio close-coupling calculation of the lower vibrational energies of the HF dimer
Chemical Physics Letters, 176 (3-4) :255-260
1991
DOI: 10.1016/0009-2614(91)90026-6; 364.
Becker, Eilhard; Benter, Thorsten; Kampf, R.; Schindler, Ralph N.; Wille, Uta
A Redetermination of the Rate Constant of the Reaction F + HNO3 → HF + NO3
Berichte der Bunsengesellschaft für physikalische Chemie, 95 (10) :1168-1173
1991
DOI: 10.1002/bbpc.19910951002; 363.
Becker, Eilhard; Benter, Thorsten; Kampf, R.; Schindler, Ralph N.; Wille, Uta
A Redetermination of the Rate Constant of the Reaction F + HNO\(_{3}\) → HF + NO\(_{3}\)
Berichte der Bunsengesellschaft für physikalische Chemie, 95 (10) :1168-1173
1991
DOI: 10.1002/bbpc.19910951002; 362.
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; 361.
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; 360.
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; 359.
Marshall, Mark D.; Jensen, Per; Bunker, Philip R.
An ab initio close-coupling calculation of the lower vibrational energies of the HF dimer
Chemical Physics Letters, 176 (3-4) :255-260
1991
DOI: 10.1016/0009-2614(91)90026-6; 358.
Jensen, Per; Marshall, Mark D.; Bunker, Philip R.; Karpfen, Alfred
An ab initio close-coupling calculation of the lower vibrational energies of the HCl dimer
Chemical Physics Letters, 180 (6) :594-600
1991
DOI: 10.1016/0009-2614(91)85016-P; 357.
Becker, Eilhard; Benter, Thorsten; Kampf, R.; Schindler, Ralph N.; Wille, Uta
A Redetermination of the Rate Constant of the Reaction F + HNO\(_{3}\) → HF + NO\(_{3}\)
Berichte der Bunsengesellschaft für physikalische Chemie, 95 (10) :1168-1173
1991
DOI: 10.1002/bbpc.19910951002; 356.
Marshall, Mark D.; Jensen, Per; Bunker, Philip R.
An ab initio close-coupling calculation of the lower vibrational energies of the HF dimer
Chemical Physics Letters, 176 (3-4) :255-260
1991
DOI: 10.1016/0009-2614(91)90026-6

Index Analysis

Group members working on that field

Cooperations

Publications

380.

379.

378.

377.

376.

375.

374.

373.

372.

371.

370.

369.

368.

367.

366.

365.

364.

363.

362.

361.

360.

359.

358.

357.

356.