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
- 2000
942.
Setzer, Klaus-Dieter; Uibel, C.; Zyrnicki, W.; Pravilov, A. M.; Fink, Ewald H.; Liebermann, Heinz-Peter; Alekseyev, Aleksey B.; Buenker, Robert J.
Experimental and Theoretical Study of the Electronic States and Spectra of BiNa
Journal of Molecular Spectroscopy, 204 (2) :163-175
2000
Herausgeber: Academic Press941.
Bartel, A.
Generalised Multirate — Two {ROW}-type Versions for Circuit simulation
Unclas- sified NatLab Report No. 2000/804
Herausgeber: Philips Electronics
2000940.
Bartel, A
Generalised multirate: Two {ROW}-type versions for circuit simulation
Unclassified NatLab Report, Eindhoven, 804 :2000
2000939.
Jacob, Birgit; Partington, Jonathan R.
Graphs, closability, and causality of linear time-invariant discrete-time systems
Internat. J. Control, 73 (11) :1051--1060
2000938.
Becker, Karl Heinz; Donner, Birgit; Freitas Dinis, Carlos M.; Geiger, Harald; Schmidt, Frank; Wiesen, Peter
Kinetics of the C\(_{2}\)(a\(^{3}\)\(\Pi\)\(_{u}\)) Radical Reacting with Selected Molecules and Atoms
Zeitschrift für Physikalische Chemie, 214 (4) :503
2000
Herausgeber: De Gruyter Oldenbourg937.
Becker, Karl Heinz; Donner, Birgit; Freitas Dinis, Carlos M.; Geiger, Harald; Schmidt, Frank; Wiesen, Peter
Kinetics of the C\(_{2}\)(a\(^{3}\)\(\Pi\)\(_{u}\)) Radical Reacting with Selected Molecules and Atoms
Zeitschrift für Physikalische Chemie, 214 (4) :503
2000
Herausgeber: De Gruyter Oldenbourg936.
Becker, Karl Heinz; Donner, Birgit; Freitas Dinis, Carlos M.; Geiger, Harald; Schmidt, Frank; Wiesen, Peter
Kinetics of the C2(a3Πu) Radical Reacting with Selected Molecules and Atoms
Zeitschrift für Physikalische Chemie, 214 (4) :503
2000
Herausgeber: De Gruyter Oldenbourg935.
Becker, Karl Heinz; Kurtenbach, Ralf; Schmidt, Frank; Wiesen, Peter
Kinetics of the NCO radical reacting with atoms and selected molecules
Combustion and Flame, 120 (4) :570-577
2000
Herausgeber: Elsevier934.
Becker, Karl Heinz; Kurtenbach, Ralf; Schmidt, Frank; Wiesen, Peter
Kinetics of the NCO radical reacting with atoms and selected molecules
Combustion and Flame, 120 (4) :570-577
2000
Herausgeber: Elsevier933.
Becker, Karl Heinz; Kurtenbach, Ralf; Schmidt, Frank; Wiesen, Peter
Kinetics of the NCO radical reacting with atoms and selected molecules
Combustion and Flame, 120 (4) :570-577
2000
Herausgeber: Elsevier932.
Günther, Michael; Hoschek, Markus
Modified ROW methods for electric circuit simulation packages
2000931.
Setzer, Klaus-Dieter; Borkowska-Burnecka, J.; Zyrnicki, W.; Fink, Ewald H.
Near-infrared electronic transitions of Pb\(_{2}\)
Journal of molecular spectroscopy, 203 (2) :244-248
2000
Herausgeber: Academic Press930.
Setzer, Klaus-Dieter; Borkowska-Burnecka, J.; Zyrnicki, W.; Fink, Ewald H.
Near-infrared electronic transitions of Pb\(_{2}\)
Journal of molecular spectroscopy, 203 (2) :244-248
2000
Herausgeber: Academic Press929.
Setzer, Klaus-Dieter; Borkowska-Burnecka, J.; Zyrnicki, W.; Fink, Ewald H.
Near-infrared electronic transitions of Pb2
Journal of molecular spectroscopy, 203 (2) :244-248
2000
Herausgeber: Academic Press928.
Schäfer, Klaus; Heland, Jörg; Lister, Dave H.; Wilson, Chris W.; Howes, Roger J.; Falk, Robert S.; Lindermeir, Erwin; Birk, Manfred; Wagner, Georg; Haschberger, Peter; Bernard, Marc; Legras, Olivier; Wiesen, Peter; Kurtenbach, Ralf; Brockmann, Klaus Josef; Kriesche, Volker; Hilton, Moira; Bishop, Gary; Clarke, Roy; Workman, John; Caola, Michael; Geatches, Rachel; Burrows, Roger; Black, John D.; Hervé, Philippe; Vally, Johanna
Nonintrusive optical measurements of aircraft engine exhaust emissions and comparison with standard intrusive techniques
Applied Optics, 39 (3) :441-455
2000927.
Sch{ä}fer, Klaus; Heland, J{ö}rg; Lister, Dave H.; Wilson, Chris W.; Howes, Roger J.; Falk, Robert S.; Lindermeir, Erwin; Birk, Manfred; Wagner, Georg; Haschberger, Peter; Bernard, Marc; Legras, Olivier; Wiesen, Peter; Kurtenbach, Ralf; Brockmann, Klaus Josef; Kriesche, Volker; Hilton, Moira; Bishop, Gary; Clarke, Roy; Workman, John; Caola, Michael; Geatches, Rachel; Burrows, Roger; Black, John D.; Herv{é}, Philippe; Vally, Johanna
Nonintrusive optical measurements of aircraft engine exhaust emissions and comparison with standard intrusive techniques
Applied Optics, 39 (3) :441-455
2000926.
Sch{ä}fer, Klaus; Heland, J{ö}rg; Lister, Dave H.; Wilson, Chris W.; Howes, Roger J.; Falk, Robert S.; Lindermeir, Erwin; Birk, Manfred; Wagner, Georg; Haschberger, Peter; Bernard, Marc; Legras, Olivier; Wiesen, Peter; Kurtenbach, Ralf; Brockmann, Klaus Josef; Kriesche, Volker; Hilton, Moira; Bishop, Gary; Clarke, Roy; Workman, John; Caola, Michael; Geatches, Rachel; Burrows, Roger; Black, John D.; Herv{é}, Philippe; Vally, Johanna
Nonintrusive optical measurements of aircraft engine exhaust emissions and comparison with standard intrusive techniques
Applied Optics, 39 (3) :441-455
2000925.
Günther, Michael; Rentrop, Peter
Numerical simulation of electrical circuits
GAMM-Mitteilungen, 23 (1-2) :51–77
2000924.
Günther, Michael; Rentrop, Peter
Numerical simulation of electrical circuits
GAMM Mitteilungen, 23 (1-2) :51--77
2000923.
Günther, Michael; Ostermann, Alexander
Numerical treatment of ordinary and algebra-differential equations
2000922.
Jacob, Birgit; Partington, Jonathan R.; Ünalmış, Banu
On discrete-time linear systems with almost-periodic kernels
J. Math. Anal. Appl., 252 (2) :549--570
2000921.
Winkler, R.
On logarithmic norms for differential algebraic equations
Preprint 00-17
Humboldt-Universität zu Berlin
2000920.
Hamacher, Horst W.; Klamroth, Kathrin
Planar Weber location problems with barriers and block norms
Annals of Operations Research, 96 :191-208
2000919.
Tyuterev, Vladimir G.; Cours, T.; Tashkun, Sergey A.; Barbe, Alain; Jensen, Per
Potential function of the ozone molecule: global calculations of the rovibrational states and the dissociation behavior
In Sinitsa, Leonid N., Editor, 13th Symposium and School on High-Resolution Molecular SpectroscopyBand4063, Seite 142
In Sinitsa, Leonid N., Editor
Herausgeber: International Society for Optics and Photonics
2000918.
Tyuterev, Vladimir G.; Cours, T.; Tashkun, Sergey A.; Barbe, Alain; Jensen, Per
Potential function of the ozone molecule: global calculations of the rovibrational states and the dissociation behavior
In Sinitsa, Leonid N., Editor, 13th Symposium and School on High-Resolution Molecular SpectroscopyBand4063, Seite 142
In Sinitsa, Leonid N., Editor
Herausgeber: International Society for Optics and Photonics
2000
