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
992.
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
2001985.
McKeachie, J. Ryan; Veer, Wytze E.; Short, Luke Chandler; Garnica, R. M.; Appel, Matthew F.; Benter, Thorsten
Selective ultra-trace detection of NO and NO\(_{2}\) in complex gas mixtures using broad-bandwidth REMPI mass spectrometry
Analyst, 126 (8) :1221-1228
2001984.
McKeachie, J. Ryan; Veer, Wytze E.; Short, Luke Chandler; Garnica, R. M.; Appel, Matthew F.; Benter, Thorsten
Selective ultra-trace detection of NO and NO\(_{2}\) in complex gas mixtures using broad-bandwidth REMPI mass spectrometry
Analyst, 126 (8) :1221-1228
2001983.
McKeachie, J. Ryan; van der Veer, Wytze E.; Short, Luke Chandler; Garnica, R. M.; Appel, Matthew F.; Benter, Thorsten
Selective ultra-trace detection of NO and NO2 in complex gas mixtures using broad-bandwidth REMPI mass spectrometry
Analyst, 126 (8) :1221-1228
2001982.
Bach, Thorsten; Kirsch, Stefan
Synthesis of 6-Substituted 4-Hydroxy-2-pyrones from Aldehydes by Addition of an Acetoacetate Equivalent, Dess-Martin Oxidation and Subsequent Cyclization
Synlett, 2001 (12) :1974–1976
2001
ISSN: 0936-5214, 1437-2096981.
Jacob, Birgit; Partington, Jonathan R.
The Weiss conjecture on admissibility of observation operators for contraction semigroups
Integral Equations Operator Theory, 40 (2) :231--243
2001980.
Bartel, Andreas; Günther, Michael
The developments in multirating for coupled systems
ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik, 81 (S3) :739–742
2001979.
Bartel, A.; G\"unther, Michael
The developments in multirating for coupled systems
Z. f. Angew. Math. u. Mech., 81 (3) :S739--S742
2001978.
Yurchenko, Sergey N.; Jensen, Per; Li, Yan; Buenker, Robert J.; Bunker, Philip R.
The near ultraviolet band system of singlet methylene
Journal of Molecular Spectroscopy, 208 (1) :136-143
2001977.
Yurchenko, Sergey N.; Jensen, Per; Li, Yan; Buenker, Robert J.; Bunker, Philip R.
The near ultraviolet band system of singlet methylene
Journal of Molecular Spectroscopy, 208 (1) :136-143
2001976.
Yurchenko, Sergey N.; Jensen, Per; Li, Yan; Buenker, Robert J.; Bunker, Philip R.
The near ultraviolet band system of singlet methylene
Journal of Molecular Spectroscopy, 208 (1) :136-143
2001975.
Tausch, Michael W.; Wachtendonk, M.
UNTERRICHTSPRAXIS S II, Band 1 ''Protolysegleichgewichte''
Herausgeber: Aulis Verlag Deubner, Köln
2001974.
Tausch, Michael W.; Woock, M.; Twellmann, M.
Vom Erdöl zum Kaugummi - ein Kontext und seine Facetten
Praxis der Naturwissenschaften - Chemie in der Schule, 50 (1) :11
2001973.
[german] Bohrmann, Claudia; Twellmann, M.; Tausch, Michael W.
Vom galvanischen Element zur Solarzelle
Naturwissenschaften im Unterricht Chemie, 66 (6) :12–16
2001972.
Jacob, Birgit
Zeros of Fredholm operator valued H^p-functions
Math. Nachr., 227 :81--97
2001- 2000
971.
Günther, Michael
A joint DAE/PDE model for interconnected electrical networks
Mathematical and Computer Modelling of Dynamical Systems, 6 :114–128
2000
Herausgeber: Taylor & Francis970.
A joint DAE/PDE model for interconnected electrical networks
Mathematical and Computer Modelling of Dynamical Systems, 6 (2) :114--128
2000
Herausgeber: Taylor \& Francis969.
Garnica, R. M.; Appel, Matthew F.; Eagan, L.; McKeachie, J. Ryan; Benter, Thorsten
A REMPI method for the ultrasensitive detection of NO and NO\(_{2}\) using atmospheric pressure laser ionization mass spectrometry
Analytical Chemistry, 72 (22) :5639-5646
2000968.
Garnica, R. M.; Appel, Matthew F.; Eagan, L.; McKeachie, J. Ryan; Benter, Thorsten
A REMPI method for the ultrasensitive detection of NO and NO\(_{2}\) using atmospheric pressure laser ionization mass spectrometry
Analytical Chemistry, 72 (22) :5639-5646
2000
