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
934.
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
2000917.
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
2000916.
Günther, Michael; Simeon, Bernd
Praktikum Wissenschaftliches Rechnen auf dem HRZ-Vektorparallelrechner VPP
2000915.
Denk, Ceorg; Günther, Michael; Kahlert, Martin; Paffrath, Meinhard; Rentrop, Peter; Wever, Utz; Zheng, Q
Recent advances in electronic industry by numerical simulation
2000914.
Günther, Michael
Semidiscretization may act like a deregularization
Mathematics and Computers in Simulation, 53 (4) :293–301
2000
Herausgeber: Elsevier913.
Günther, Michael
Semidiscretization may act like a deregularization
Mathematics and computers in simulation, 53 (4-6) :293--301
2000
Herausgeber: North-Holland912.
Kleffmann, Jörg; Becker, Karl Heinz; Br{ö}ske, Rolf; Rothe, Dieter; Wiesen, Peter
Solubility of HBr in H\(_{2}\)SO\(_{4}\)/H\(_{2}\)O and HNO\(_{3}\)/H\(_{2}\)SO\(_{4}\)/H\(_{2}\)O Solutions
The Journal of Physical Chemistry A, 104 (37) :8489-8495
2000911.
Kleffmann, Jörg; Becker, Karl Heinz; Br{ö}ske, Rolf; Rothe, Dieter; Wiesen, Peter
Solubility of HBr in H\(_{2}\)SO\(_{4}\)/H\(_{2}\)O and HNO\(_{3}\)/H\(_{2}\)SO\(_{4}\)/H\(_{2}\)O Solutions
The Journal of Physical Chemistry A, 104 (37) :8489-8495
2000910.
Kleffmann, Jörg; Becker, Karl Heinz; Bröske, Rolf; Rothe, Dieter; Wiesen, Peter
Solubility of HBr in H2SO4/H2O and HNO3/H2SO4/H2O Solutions
The Journal of Physical Chemistry A, 104 (37) :8489-8495
2000
