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
- 2002
1106.
Odaka, Tina Erica; Hirano, Tsuneo; Jensen, Per
An ab initio study of the A~ 2Π state and the A~ 2Π ← X~ 2Σ+ electronic transition of MgNC
Journal of Molecular Spectroscopy, 211 (1) :147-161
20021105.
Tausch, Michael W.; Bohrmann, Claudia; Seesing, Michael
Eine no-cost Brennstoffzelle
Praxis der Naturwissenschaften - Chemie in der Schule, 51 (6)
20021104.
Bohrmann-Linde, Claudia
Labothek Duisburg
Praxis der Naturwissenschaften - Chemie in der Schule, 51 (8)
20021103.
[german] Bohrmann, Claudia; Tausch, Michael W.
Elektrochemolumineszenz mit unbedenklichen Chemikalien: Das leuchtende Scherblatt
Chemie in unserer Zeit, 36 (3) :164--167
2002
Herausgeber: Wiley1102.
Scientific Papers-Sound Propagation Modeling-Efficient Numerical Implementation of Discrete Transparent Boundary Conditions for Parabolic Equations in Underwater Acoustics
Acustica-Stuttgart, 88 (5) :711--713
2002
Herausgeber: Stuttgart [Germany]: S. Hirzel, 1951-1995.- 2001--2002
1101.
Arnold, A.; Ehrhardt, M.; Rjasanow, S.
Numerik partieller Differential\-gleichungen
Vorlesungsskript, Universität Saarbrücken, WS2001/02
2001--2002- 2001
1100.
[german] Bohrmann, Claudia; Twellmann, M.; Tausch, Michael W.
Vom galvanischen Element zur Solarzelle
Naturwissenschaften im Unterricht Chemie, 66 (6) :12–16
20011099.
Jacob, Birgit; Zwart, Hans
Exact observability of diagonal systems with a finite-dimensional output operator
Systems Control Lett., 43 (2) :101--109
20011098.
[german] Bohrmann, Claudia; Tausch, Michael W.
Hypermedia-Baustein: Photoelektrochemische Zelle
Praxis der Naturwissenschaften - Chemie in der Schule, 50 (7)
20011097.
Jacob, Birgit; Partington, Jonathan R.
On the boundedness and continuity of the spectral factorization mapping
SIAM J. Control Optim., 40 (1) :88--106
20011096.
Jacob, Birgit
Zeros of Fredholm operator valued H^p-functions
Math. Nachr., 227 :81--97
20011095.
Woock, Michael; Tausch, Michael W.
Es tropft, Herr Lehrer - die Synthese von {MTBE} im Schulexperiment
{CHEMKON}, 8 (2) :86--90
2001
Herausgeber: Wiley1094.
Jacob, Birgit; Partington, Jonathan R.
The Weiss conjecture on admissibility of observation operators for contraction semigroups
Integral Equations Operator Theory, 40 (2) :231--243
20011093.
Farkas, Bálint; Matolcsi, Máté
Commutation properties of the form sum of positive, symmetric operators
Acta Sci. Math. (Szeged), 67 (3-4) :777-790
20011092.
Jacob, Birgit; Zwart, Hans
Exact observability of diagonal systems with a one-dimensional output operator
, Band 11
Seite 1277--1283
2001
1277--12831091.
Jacob, Birgit; Zwart, Hans
Exact controllability of C_0-groups with one-dimensional input operators
Advances in mathematical systems theory aus Systems Control Found. Appl.
Seite 221--242
Herausgeber: Birkhäuser Boston, Boston, MA
2001
221--2421090.
[german] Tausch, Michael W.; Woock, M.
Hypermedia-Baustein: MTBE im Kraftstoff
Praxis der Naturwissenschaften - Chemie in der Schule, 50 (7) :24
20011089.
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
20011088.
Jørgensen, Uffe G.; Jensen, Per; Sørensen, G. O.; Aringer, B.
H2O in stellar atmospheres
Astronomy & Astrophysics, 372 (1) :249-259
2001
Herausgeber: EDP Sciences1087.
Favier, Fr{é}d{é}ric; Walter, Erich C.; Zach, Michael P.; Benter, Thorsten; Penner, Reginald M.
Hydrogen Sensors and Switches from Electrodeposited Palladium Mesowire Arrays
Science, 293 (5538) :2227-2231
20011086.
Kurtenbach, Ralf; Becker, Karl Heinz; Gomes, J. A. G.; Kleffmann, Jörg; L{ö}rzer, Jutta C.; Spittler, M.; Wiesen, Peter; Ackermann, R.; Geyer, Andreas; Platt, Ulrich
Investigations of emissions and heterogeneous formation of HONO in a road traffic tunnel
Atmospheric Environment, 35 (20) :3385-3394
2001
Herausgeber: Pergamon1085.
Favier, Frédéric; Walter, Erich C.; Zach, Michael P.; Benter, Thorsten; Penner, Reginald M.
Hydrogen Sensors and Switches from Electrodeposited Palladium Mesowire Arrays
Science, 293 (5538) :2227-2231
20011084.
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, Canada1083.
Kurtenbach, Ralf; Becker, Karl Heinz; Gomes, J. A. G.; Kleffmann, Jörg; Lörzer, Jutta C.; Spittler, M.; Wiesen, Peter; Ackermann, R.; Geyer, Andreas; Platt, Ulrich
Investigations of emissions and heterogeneous formation of HONO in a road traffic tunnel
Atmospheric Environment, 35 (20) :3385-3394
2001
Herausgeber: Pergamon1082.
Freitas Dinis, Carlos M.; Geiger, Harald; Wiesen, Peter
Kinetics of the reactions of OH(X\(^{2}\)\(\Pi\)) radicals with 1,3-dioxolane selected dialkoxy methanes
Physical Chemistry Chemical Physics, 3 (14) :2831-2835
2001
