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

1993: 425.
Jensen, Per; Kozin, Igor N.
The Potential Energy Surface for the Electronic Ground State of H\(_{2}\)Se Derived from Experiment
Journal of Molecular Spectroscopy, 160 (1) :39-57
1993
Herausgeber: Academic Press
DOI: 10.1006/jmsp.1993.1155; 424.
Jensen, Per; Kozin, Igor N.
The Potential Energy Surface for the Electronic Ground State of H\(_{2}\)Se Derived from Experiment
Journal of Molecular Spectroscopy, 160 (1) :39-57
1993
Herausgeber: Academic Press
DOI: 10.1006/jmsp.1993.1155; 423.
Jensen, Per; Kozin, Igor N.
The Potential Energy Surface for the Electronic Ground State of H2Se Derived from Experiment
Journal of Molecular Spectroscopy, 160 (1) :39-57
1993
Herausgeber: Academic Press
DOI: 10.1006/jmsp.1993.1155; 422.
Chong, Delano P.; Papousek, Dusan; Chen, Yit-Tsong; Jensen, Per
Theoretical vibrational and rotational energies and intensities of the HNSi and DNSi molecules
The Journal of Chemical Physics, 98 (2) :1352-1357
1993
DOI: 10.1063/1.464302; 421.
Chong, Delano P.; Papousek, Dusan; Chen, Yit-Tsong; Jensen, Per
Theoretical vibrational and rotational energies and intensities of the HNSi and DNSi molecules
The Journal of Chemical Physics, 98 (2) :1352-1357
1993
DOI: 10.1063/1.464302; 420.
Chong, Delano P.; Papousek, Dusan; Chen, Yit-Tsong; Jensen, Per
Theoretical vibrational and rotational energies and intensities of the HNSi and DNSi molecules
The Journal of Chemical Physics, 98 (2) :1352-1357
1993
DOI: 10.1063/1.464302; 419.
Günther, Michael; Rentrop, R
TUM
1993; 418.
Tausch, Michael W.
Unterrichtsmodell Ozon
FWU Magazin (3-4) :20
1993; 417.
Maten, E. J. W.; Huijben, A. J. M.
Vector extrapolation applied to a time cyclic heat problem
In Lewis, R. W., Editor, Numerical methods in thermal problemsBand8(2), Seite 983-994
In Lewis, R. W., Editor
Herausgeber: Pineridge Press Lmt, Swansea, UK
1993; 416.
Barclay, V. J.; Hamilton, I. P.; Jensen, Per
Vibrational levels for the lowest-lying triplet and singlet states of CH\(_{2}\) and NH\(_{2}\)\(^{+}\)
The Journal of Chemical Physics, 99 (12) :9709-9719
1993
DOI: 10.1063/1.465453; 415.
Barclay, V. J.; Hamilton, I. P.; Jensen, Per
Vibrational levels for the lowest-lying triplet and singlet states of CH\(_{2}\) and NH\(_{2}\)\(^{+}\)
The Journal of Chemical Physics, 99 (12) :9709-9719
1993
DOI: 10.1063/1.465453; 414.
Barclay, V. J.; Hamilton, I. P.; Jensen, Per
Vibrational levels for the lowest-lying triplet and singlet states of CH2 and NH2+
The Journal of Chemical Physics, 99 (12) :9709-9719
1993
DOI: 10.1063/1.465453
1992: 413.
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; 412.
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; 411.
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; 410.
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; 409.
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; 408.
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; 407.
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; 406.
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; 405.
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; 404.
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; 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, 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; 401.
Heilmann, Margareta
Erhöhung der Konvergenzgeschwindigkeit bei der Approximation von Funktionen mit Hilfe von Linearkombinationen spezieller positiver linearer Operatoren
Universität Dortmund
1992
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Index Analysis

Group members working on that field

Cooperations

Publications

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424.

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422.

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401.