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
- 2001
1010.
Denk, Georg; Günther, Michael; Simeon, Bernd
Numerische Simulation in Chip-Design und Fahrzeugtechnik
20011009.
Jacob, Birgit; Partington, Jonathan R.
On the boundedness and continuity of the spectral factorization mapping
SIAM J. Control Optim., 40 (1) :88--106
20011008.
Günther, Michael
Partielle differential-algebraische Systeme in der numerischen Zeitbereichsanalyse elektrischer Schaltungen
VDI-Verlag
20011007.
Günther, Michael; Hoschek, Markus
Partitionierung Strategies in Circuit Simulation
20011006.
Günther, Michael; Rentrop, Peter
PDAE-Netzwerkmodelle in der elektrischen Schaltungssimulation
:31-38
2001
Herausgeber: Frankfurt1005.
Klamroth, Kathrin
Planar location problems with line barriers
Optimization, 49 :517-527
20011004.
Arnold, Martin; Günther, Michael
Preconditioned dynamic iteration for coupled differential-algebraic systems
BIT Numerical Mathematics, 1 (41) :1–25
2001
Herausgeber: Springer Netherlands1003.
Arnold, Martin; Günther, Michael
Preconditioned dynamic iteration for coupled differential-algebraic systems
BIT Numerical Mathematics, 41 (41) :1--25
2001
Herausgeber: Kluwer Academic Publishers1002.
Bunker, Philip R.; Chan, M. C.; Kraemer, Wolfgang P.; Jensen, Per
Predicted rovibronic spectra of CH\(_{2}\)\(^{+}\) and CD\(_{2}\)\(^{+}\)
Chemical Physics Letters, 341 (3-4) :358-362
20011001.
Bunker, Philip R.; Chan, M. C.; Kraemer, Wolfgang P.; Jensen, Per
Predicted rovibronic spectra of CH\(_{2}\)\(^{+}\) and CD\(_{2}\)\(^{+}\)
Chemical Physics Letters, 341 (3-4) :358-362
20011000.
Bunker, Philip R.; Chan, M. C.; Kraemer, Wolfgang P.; Jensen, Per
Predicted rovibronic spectra of CH2+ and CD2+
Chemical Physics Letters, 341 (3-4) :358-362
2001999.
Jensen, Per; Buenker, Robert J.; Gu, Jian-ping; Osmann, Gerald; Bunker, Philip R.
Refined potential-energy surfaces for the X\verb=~=\(^{2}\)A'' and A\verb=~=\(^{2}\)A' electronic states of the HO\(_{2}\) molecule
Canadian Journal of Physics, 79 (2-3) :641-652
2001
Herausgeber: NRC Research Press Ottawa, Canada998.
Jensen, Per; Buenker, Robert J.; Gu, Jian-ping; Osmann, Gerald; Bunker, Philip R.
Refined potential-energy surfaces for the X\verb=~=\(^{2}\)A'' and A\verb=~=\(^{2}\)A' electronic states of the HO\(_{2}\) molecule
Canadian Journal of Physics, 79 (2-3) :641-652
2001
Herausgeber: NRC Research Press Ottawa, Canada997.
Jensen, Per; Buenker, Robert J.; Gu, Jian-ping; Osmann, Gerald; Bunker, Philip R.
Refined potential-energy surfaces for the X~2A" and A~2A' electronic states of the HO2 molecule
Canadian Journal of Physics, 79 (2-3) :641-652
2001
Herausgeber: NRC Research Press Ottawa, Canada996.
Lampe, S.; Brachtendorf, H. G.; Maten, E. J. W.; Onneweer, S. P.; Laur, R.
Robust Limit Cycle Calculations of Oscillators
Lecture Notes in Computational Science and Engineering
Seite 233--240
Herausgeber: Springer Berlin Heidelberg
2001
233--240995.
Günther, M.; Hoschek, M.; Weiner, R.
ROW methods adapted to a cheap Jacobian
Applied Numerical Mathematics, 37 (1) :231–240
2001
Herausgeber: Elsevier994.
Günther, Michael; Hoschek, Markus; Weiner, R
ROW methods adapted to a cheap Jacobian
Applied numerical mathematics, 37 (1-2) :231--240
2001
Herausgeber: North-Holland993.
G\"unther, Michael; Hoschek, M.; Weiner, R.
ROW methods adapted to a cheap Jacobian}
APNUM, 37 :231-240
2001992.
Günther, Michael; Hoschek, Markus
ROW-type Integration Methods for Circuit Simulation Packages
:448-455
2001
Herausgeber: B.G. Teubner, Stuttgart991.
Hecht, Dirk; Günther, Michael; Rienen, Ursula
Scientific Computing in Electrical Engineering: Proceedings
Herausgeber: Springer
2001990.
Scientific Computing in Electrical Engineering: Proceedings of the 3rd International Workshop, 20-23 August 2000, Warnemünde, Germany
In Rienen, Ursula and Günther, Michael and Hecht, Dirk, Editor aus Lecture Notes in Computational Science and Engineering
Herausgeber: Springer Berlin Heidelberg
2001ISBN: 978-3-540-42173-3
989.
Van Rienen, Ursula; Günther, Michael; Hecht, Dirk
Scientific Computing in Electrical Engineering: Proceedings of the 3rd International Workshop, August 20--23, 2000, Warnemünde, Germany
2001988.
Rienen, Ursula van; Günther, Michael; Hecht, Dirk
Scientific computing in electrical engineering: proceedings of the 3rd International Workshop, August 20-23, 2000, Warnemünde, Germany
(No Title)
2001987.
Scientific Computing in Electrical Engineering. Proceedings of the 3rd International Workshop, 20-23 August 2000, Warnem\"unde, Germany
In {van Rienen}, U. and G\"unther, M. and Hecht, D., Editor aus Lecture Notes in Computational Science and Engineering
Herausgeber: Springer-Verlag, Berlin
2001986.
Tausch, Michael W.
Sclüsselexperimente - Kreuzungen, Brücken und Pässe im Chemieunterricht
Praxis der Naturwissenschaften - Chemie in der Schule, 50 (3) :1
2001
