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

1993

428.

Biggs, P.; Canosa-Mas, Carlos E.; Monks, P. S.; Wayne, Richard P.; Benter, Thorsten; Schindler, Ralph N.
The kinetics of the nitrate radical self-reaction
International Journal of Chemical Kinetics, 25 (10) :805-817
1993

DOI: 10.1002/kin.550251002

427.

Biggs, P.; Canosa-Mas, Carlos E.; Monks, P. S.; Wayne, Richard P.; Benter, Thorsten; Schindler, Ralph N.
The kinetics of the nitrate radical self-reaction
International Journal of Chemical Kinetics, 25 (10) :805-817
1993

DOI: 10.1002/kin.550251002

426.

Biggs, P.; Canosa-Mas, Carlos E.; Monks, P. S.; Wayne, Richard P.; Benter, Thorsten; Schindler, Ralph N.
The kinetics of the nitrate radical self-reaction
International Journal of Chemical Kinetics, 25 (10) :805-817
1993

DOI: 10.1002/kin.550251002

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.

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

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.

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

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; 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

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; 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

404.

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