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
462.
Günther, Michael; Rentrop, R
TUM
1993461.
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
1993460.
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
1993459.
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
1993458.
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 Press457.
J{\o}rgensen, Uffe G.; Jensen, Per
The Dipole Moment Surface and the Vibrational Transition Moments of H\(_{2}\)O
Journal of Molecular Spectroscopy, 161 (1) :219-242
1993
Herausgeber: Academic Press456.
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 Press455.
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 Press454.
Denk, G.; G\"unther, Michael; Schmidt, W.
Olympische Chips: Schaltkreise -- Spannung in der Numerik
Technische Universit\"at M\"unchen, TUM-Sonderreihe Forschung f\"ur Bayern, Heft 6: Fakult\"at f\"ur Mathematik, Fakult\"at f\"ur Informatik, Seite 14--15
1993453.
Denk, G.; Günther, M.; Schmidt, W.
Olympische Chips: Schaltkreise - Spannung in der Numerik
1993452.
Günther, Michael; Rentrop, Peter
Multirate ROW methods and latency of electric circuits
Applied Numerical Mathematics, 13 (1-3) :83--102
1993
Herausgeber: North-Holland451.
Günther, Michael; Rentrop, Peter
Multirate ROW methods and latency of electric circuits
Applied Numerical Mathematics, 13 (1) :83–102
1993
Herausgeber: Elsevier450.
G\"unther, Michael; Rentrop, P.
Multirate {ROW} methods and latency of electric circuits
Appl.~Numer.~Math., 13 :83--102
1993449.
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
1993448.
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 Press447.
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 Press446.
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
1993445.
Günther, Michael; Rentrop, Peter
Partitioning and multirate strategies in latent electric circuits
1993444.
Günther, Michael
Charge-oriented modelling of electric circuits and Rosenbrock-Wanner methods
Herausgeber: Mathematisches Institut und Institut für Informatik der Technischen~…
1993443.
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 Press442.
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 Press441.
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 Press440.
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.439.
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.438.
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.
