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: 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; 367.
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; 366.
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; 365.
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; 364.
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; 363.
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; 362.
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; 361.
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; 360.
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; 359.
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; 358.
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; 357.
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; 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; 355.
Karpfen, Alfred; Bunker, Philip R.; Jensen, Per
An ab initio study of the hydrogen chloride dimer: the potential energy surface and the characterization of the stationary points
Chemical Physics, 149 (3) :299-309
1991
DOI: 10.1016/0301-0104(91)90029-S

Index Analysis

Group members working on that field

Cooperations

Publications

379.

378.

377.

376.

375.

374.

373.

372.

371.

370.

369.

368.

367.

366.

365.

364.

363.

362.

361.

360.

359.

358.

357.

356.

355.