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
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 Press454.
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 Press453.
Maten, E. J. W.
Simulation of radiation heat transfer in television tubes
In R. W. Lewis, Editor, Numerical methods in thermal problemsBand8(1), Seite 831-842
In R. W. Lewis, Editor
Herausgeber: Pineridge Press Lmt, Swansea, UK
1993452.
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
1993451.
Günther, Michael
Charge-oriented modelling of electric circuits and Rosenbrock-Wanner methods
Herausgeber: Mathematisches Institut und Institut für Informatik der Technischen~…
1993450.
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 Press449.
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 Press448.
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 Press447.
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.446.
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.445.
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.444.
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 Press443.
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 Press442.
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 Press441.
Schilders, W. H. A.; Maten, E. J. W.; Rusch, J. J.; Heynderickx, I. E. J.
Simulation of non-isothermal Couette flow of liquid crystalline polymers
In Taylor, C., Editor, Numerical methods in laminar and turbulent flowBand8(1), Seite 480-491
In Taylor, C., Editor
Herausgeber: Pineridge Press Lmt, Swansea, UK
1993440.
Maten, E. J. W.; Heynderickx, I. E. J.; Potze, W.; Rusch, J. J.; Schilders, W. H. A.
Simulation of steady non-isothermal flow of liquid crystalline polymers
In K. Morgan and E. Onate and J. Periaux and J. Peraire and O. C. Zienkiewicz, Editor, Finite elements in fluids, New trends and applicationsBand1, Seite 572-581
In K. Morgan and E. Onate and J. Periaux and J. Peraire and O. C. Zienkiewicz, Editor
Herausgeber: Centro Int. de Metodos Num. en Ing. (CIMNE), Barcelona and Pineridge Press Lmt, Swansea, UK
1993439.
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
1993438.
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
1993437.
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
1993436.
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
1993435.
Tausch, Michael W.
Unterrichtsmodell Ozon
FWU Magazin (3-4) :20
1993434.
Günther, Michael; Rentrop, R
TUM
1993433.
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
1993432.
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
1993431.
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
