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 Press474.
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 Press473.
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
1994472.
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
1994471.
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
1994470.
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- 1993
469.
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 Press468.
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 Press467.
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 Press466.
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.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.464.
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.463.
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 Press462.
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 Press461.
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 Press460.
Günther, Michael
Charge-oriented modelling of electric circuits and Rosenbrock-Wanner methods
Herausgeber: Mathematisches Institut und Institut für Informatik der Technischen~…
1993459.
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
1993458.
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 Press457.
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 Press456.
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 Press455.
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
1993454.
G\"unther, Michael; Rentrop, P.
Multirate {ROW} methods and latency of electric circuits
Appl.~Numer.~Math., 13 :83--102
1993453.
Günther, Michael; Rentrop, Peter
Multirate ROW methods and latency of electric circuits
Applied Numerical Mathematics, 13 (1) :83–102
1993
Herausgeber: Elsevier452.
Günther, Michael; Rentrop, Peter
Multirate ROW methods and latency of electric circuits
Applied Numerical Mathematics, 13 (1-3) :83--102
1993
Herausgeber: North-Holland451.
Denk, G.; Günther, M.; Schmidt, W.
Olympische Chips: Schaltkreise - Spannung in der Numerik
1993
