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

1994

475.

Jensen, Per; Bunker, Philip R.
The Molecular Symmetry Group for Molecules in High Angular Momentum States
Journal of Molecular Spectroscopy, 164 (1) :315-317
1994
Herausgeber: Academic Press

DOI: 10.1006/JMSP.1994.1075

474.

Jensen, Per; Bunker, Philip R.
The Molecular Symmetry Group for Molecules in High Angular Momentum States
Journal of Molecular Spectroscopy, 164 (1) :315-317
1994
Herausgeber: Academic Press

DOI: 10.1006/JMSP.1994.1075

473.

Bednarek, G.; Wayne, R.P.; Wildt, J{ü}rgen; Fink, E.H.
The yield of O\(_{2}\)(b \(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\), v=0) produced by quenching of O\(_{2}\)(A \(^{3}\)\(\Sigma\)\(_{u}\)\(^{+}\), v=8) by O\(_{2}\)
Chemical Physics, 185 (2) :251-261
1994

DOI: 10.1016/0301-0104(94)00127-8

472.

Bednarek, G.; Wayne, R.P.; Wildt, J{ü}rgen; Fink, E.H.
The yield of O\(_{2}\)(b \(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\), v=0) produced by quenching of O\(_{2}\)(A \(^{3}\)\(\Sigma\)\(_{u}\)\(^{+}\), v=8) by O\(_{2}\)
Chemical Physics, 185 (2) :251-261
1994

DOI: 10.1016/0301-0104(94)00127-8

471.

Bednarek, G.; Wayne, R.P.; Wildt, Jürgen; Fink, E.H.
The yield of O2(b 1Σg+, v=0) produced by quenching of O2(A 3Σu+, v=8) by O2
Chemical Physics, 185 (2) :251-261
1994

DOI: 10.1016/0301-0104(94)00127-8

470.

Auwera, J. Vander; Holland, J. K.; Jensen, Per; Johns, John W. C.
The ν6 band system of C3O2 near 540 cm-1
Journal of Molecular Spectroscopy, 163 (2) :529-540
1994
Herausgeber: Academic Press

DOI: 10.1006/jmsp.1994.1045

1993

469.

Janssen, H. H. J. M.; Maten, E. J. W.; Houwelingen, D.
Simulation of coupled electromagnetic and heat dissipation problems
, IEE, Colloquium on Coupling Electromagnetic to Other FieldsBand1993 / 117, Seite 3/1-3/3
Herausgeber: Institute of Electrical and Electronics Engineers ({IEEE})
Mai 1993

DOI: 10.1109/20.312651

468.

Graf, J.; Jensen, Per
A Theoretical Model for the Rotation and Vibration of Symmetrical Triatomic Molecules with Strong Coupling Between the Local Stretching Modes
Journal of Molecular Spectroscopy, 159 (1) :175-191
1993
Herausgeber: Academic Press

DOI: 10.1006/JMSP.1993.1116

467.

Graf, J.; Jensen, Per
A Theoretical Model for the Rotation and Vibration of Symmetrical Triatomic Molecules with Strong Coupling Between the Local Stretching Modes
Journal of Molecular Spectroscopy, 159 (1) :175-191
1993
Herausgeber: Academic Press

DOI: 10.1006/JMSP.1993.1116

466.

Graf, J.; Jensen, Per
A Theoretical Model for the Rotation and Vibration of Symmetrical Triatomic Molecules with Strong Coupling Between the Local Stretching Modes
Journal of Molecular Spectroscopy, 159 (1) :175-191
1993
Herausgeber: Academic Press

DOI: 10.1006/JMSP.1993.1116

465.

Cespiva, Ladislav; Bonacic-Kouteck{{\'y}}, Vlasta; Kouteck{{\'y}}, Jaroslav; Jensen, Per; Hrouda, Vojtech; C{{\'a}}rsky, Petr; Spirko, Vladim{í}r; Hobza, Pavel
Ab initio Calculations of the Rotation-Vibration Spectrum of Na\(_{3}\)\(^{+}\)
Collection of Czechoslovak Chemical Communications, 58 (1) :24-28
1993
Herausgeber: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

DOI: 10.1135/cccc19930024

464.

Cespiva, Ladislav; Bonacic-Kouteck{{\'y}}, Vlasta; Kouteck{{\'y}}, Jaroslav; Jensen, Per; Hrouda, Vojtech; C{{\'a}}rsky, Petr; Spirko, Vladim{í}r; Hobza, Pavel
Ab initio Calculations of the Rotation-Vibration Spectrum of Na\(_{3}\)\(^{+}\)
Collection of Czechoslovak Chemical Communications, 58 (1) :24-28
1993
Herausgeber: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

DOI: 10.1135/cccc19930024

463.

Cespiva, Ladislav; Bonacic-Koutecký, Vlasta; Koutecký, Jaroslav; Jensen, Per; Hrouda, Vojtech; Cársky, Petr; Spirko, Vladimír; Hobza, Pavel
Ab initio Calculations of the Rotation-Vibration Spectrum of Na3+
Collection of Czechoslovak Chemical Communications, 58 (1) :24-28
1993
Herausgeber: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

DOI: 10.1135/cccc19930024

462.

Bunker, Philip R.; Jensen, Per; Althorpe, Stuart C.; Clary, David C.
An ab initio Calculation of the Low Rotation-Vibration Energies of the CO Dimer
Journal of Molecular Spectroscopy, 157 (1) :208-219
1993
Herausgeber: Academic Press

DOI: 10.1006/JMSP.1993.1017

461.

Bunker, Philip R.; Jensen, Per; Althorpe, Stuart C.; Clary, David C.
An ab initio Calculation of the Low Rotation-Vibration Energies of the CO Dimer
Journal of Molecular Spectroscopy, 157 (1) :208-219
1993
Herausgeber: Academic Press

DOI: 10.1006/JMSP.1993.1017

460.

Bunker, Philip R.; Jensen, Per; Althorpe, Stuart C.; Clary, David C.
An ab initio Calculation of the Low Rotation-Vibration Energies of the CO Dimer
Journal of Molecular Spectroscopy, 157 (1) :208-219
1993
Herausgeber: Academic Press

DOI: 10.1006/JMSP.1993.1017

459.

Günther, Michael
Charge-oriented modelling of electric circuits and Rosenbrock-Wanner methods
Herausgeber: Mathematisches Institut und Institut für Informatik der Technischen~…
1993

458.

Tausch, Michael W.; Wachtendonk, M.; Deissenberger, H.; Porth, H.-R.; G. Weißenhorn, R.
CHEMIE S II STOFF-FORMEL-UMWELT, Lehrbuch für Grund- und Leistungskurse, 446 Seiten
Herausgeber: C. C. Buchner, Bamberg
1993

457.

Kozin, Igor N.; Jensen, Per
Fourfold Clusters of Rovibrational Energy Levels in the Fundamental Vibrational States of H\(_{2}\)Se
Journal of molecular spectroscopy, 161 (1) :186-207
1993
Herausgeber: Academic Press

DOI: 10.1006/jmsp.1993.1226

456.

Kozin, Igor N.; Jensen, Per
Fourfold Clusters of Rovibrational Energy Levels in the Fundamental Vibrational States of H\(_{2}\)Se
Journal of molecular spectroscopy, 161 (1) :186-207
1993
Herausgeber: Academic Press

DOI: 10.1006/jmsp.1993.1226

455.

Kozin, Igor N.; Jensen, Per
Fourfold Clusters of Rovibrational Energy Levels in the Fundamental Vibrational States of H2Se
Journal of molecular spectroscopy, 161 (1) :186-207
1993
Herausgeber: Academic Press

DOI: 10.1006/jmsp.1993.1226

454.

Tausch, Michael W.; Wachtendonk, M.; Deissenberger, H.; Porth, H.-R.; G. Weißenhorn, R.
Lehrerband mit didaktischen Hinweisen und Lösungen zu den Aufgaben zu CHEMIE S II STOFF-FORMEL-UMWELT, Lehrbuch für Grund- und Leistungskurse
Herausgeber: C. C. Buchner, Bamberg
1993

453.

G\"unther, Michael; Rentrop, P.
Multirate {ROW} methods and latency of electric circuits
Appl.~Numer.~Math., 13 :83--102
1993

452.

Günther, Michael; Rentrop, Peter
Multirate ROW methods and latency of electric circuits
Applied Numerical Mathematics, 13 (1) :83–102
1993
Herausgeber: Elsevier

DOI: 10.1016/0168-9274(93)90133-C

451.

Günther, Michael; Rentrop, Peter
Multirate ROW methods and latency of electric circuits
Applied Numerical Mathematics, 13 (1-3) :83--102
1993
Herausgeber: North-Holland