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
- 2003
1168.
Kirsch, Stefan; Bach, Thorsten
Stereoselective Synthesis of Enantiomerically Pure, Orthogonally Protected 2-Methylenecyclohexane-1,3,5-triols and 2,4,6-Trihydroxycyclohexanones
Synthesis, 2003 (12) :1827–1836
2003
ISSN: 0039-7881, 1437-210X1167.
Römisch, W.; Winkler, R.
Stochastic {DAEs} in circuit simulation
In Antreich, K. and Bulirsch, R. and Gilg, A. and Rentrop, P., Editor, Modeling, Simulation and Optimization of Integrated Circuits, Seite 303--318
In Antreich, K. and Bulirsch, R. and Gilg, A. and Rentrop, P., Editor
Herausgeber: Birkhäuser, Basel
20031166.
Winkler, R.
Stochastic Differential Algebraic Equations of Index 1 and Applications in Circuit Simulation
J. Comp. Math. Appl., 157 :477--505
20031165.
Tausch, Michael W.; Wachtendonk, M.; Porth, H.-R.; Schulze, I.; Wambach, H.
STOFF-FORMEL-UMWELT, Chemie für Schjg. 8 in Niedersachsen
Herausgeber: C. C. Buchner, Bamberg
20031164.
Setzer, Klaus-Dieter; Kalb, M.; Fink, Ewald H.
The a\(^{1}\)\(\Delta\)\(_{g}\) → X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\) magnetic dipole transition of S\(_{2}\)
Journal of Molecular Spectroscopy, 221 (1) :127-130
2003
Herausgeber: Academic Press1163.
Setzer, Klaus-Dieter; Kalb, M.; Fink, Ewald H.
The a\(^{1}\)\(\Delta\)\(_{g}\) → X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\) magnetic dipole transition of S\(_{2}\)
Journal of Molecular Spectroscopy, 221 (1) :127-130
2003
Herausgeber: Academic Press1162.
Setzer, Klaus-Dieter; Dorn, A.; Lorenz, Matthias; Fink, Ewald H.
The a\(^{1}\)\(\Delta\)\(_{g}\)(a2\(_{g}\)) → X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\)(X\(_{2}\)1\(_{g}\)) transition of Se\(_{2}\)
Journal of Molecular Spectroscopy, 221 (1) :13-18
2003
Herausgeber: Academic Press1161.
Setzer, Klaus-Dieter; Dorn, A.; Lorenz, Matthias; Fink, Ewald H.
The a\(^{1}\)\(\Delta\)\(_{g}\)(a2\(_{g}\)) → X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\)(X\(_{2}\)1\(_{g}\)) transition of Se\(_{2}\)
Journal of Molecular Spectroscopy, 221 (1) :13-18
2003
Herausgeber: Academic Press1160.
Setzer, Klaus-Dieter; Kalb, M.; Fink, Ewald H.
The a1Δg → X3Σg- magnetic dipole transition of S2
Journal of Molecular Spectroscopy, 221 (1) :127-130
2003
Herausgeber: Academic Press1159.
Setzer, Klaus-Dieter; Dorn, A.; Lorenz, Matthias; Fink, Ewald H.
The a1Δg(a2g) → X3Σg-(X21g) transition of Se2
Journal of Molecular Spectroscopy, 221 (1) :13-18
2003
Herausgeber: Academic Press1158.
Geiger, Harald; Barnes, Ian; Bejan, Iustinian; Benter, Thorsten; Spittler, M.
The tropospheric degradation of isoprene: an updated module for the regional atmospheric chemistry mechanism
Atmospheric Environment, 37 (11) :1503-1519
20031157.
Geiger, Harald; Barnes, Ian; Bejan, Iustinian; Benter, Thorsten; Spittler, M.
The tropospheric degradation of isoprene: an updated module for the regional atmospheric chemistry mechanism
Atmospheric Environment, 37 (11) :1503-1519
20031156.
Geiger, Harald; Barnes, Ian; Bejan, Iustinian; Benter, Thorsten; Spittler, M.
The tropospheric degradation of isoprene: an updated module for the regional atmospheric chemistry mechanism
Atmospheric Environment, 37 (11) :1503-1519
20031155.
Kirsch, Stefan; Bach, Thorsten
Total Synthesis of (+)-Wailupemycin B
Angewandte Chemie International Edition, 42 (38) :4685–4687
2003
ISSN: 1433-7851, 1521-37731154.
Jensen, Per; Kraemer, Wolfgang P.; Bunker, Philip R.
Transition moments and NH\(_{2}\) cometary spectra
Molecular Physics, 101 (4-5) :613-622
2003
Herausgeber: Taylor \& Francis Group1153.
Jensen, Per; Kraemer, Wolfgang P.; Bunker, Philip R.
Transition moments and NH\(_{2}\) cometary spectra
Molecular Physics, 101 (4-5) :613-622
2003
Herausgeber: Taylor \& Francis Group1152.
Jensen, Per; Kraemer, Wolfgang P.; Bunker, Philip R.
Transition moments and NH2 cometary spectra
Molecular Physics, 101 (4-5) :613-622
2003
Herausgeber: Taylor & Francis Group1151.
Klamroth, Kathrin; Tind, Jørgen; Wiecek, Margaret M.
Unbiased approximation in multicriteria optimization
Mathematical Methods of Operations Research, 56 :413-437
20031150.
Tausch, Michael W.; Wachtendonk, M.
UNTERRICHTSPRAXIS S II, Band 2 ''Elektrochemische Stromquellen''
Herausgeber: Aulis Verlag Deubner, Köln
20031149.
Tausch, Michael W.
Wasserstoff - der Spitzenreiter unter den Elementen
Praxis der Naturwissenschaften - Chemie in der Schule, 53 (3) :1
20031148.
Zwart, Hans; Jacob, Birgit; Staffans, Olof
Weak admissibility does not imply admissibility for analytic semigroups
, Band 48
Seite 341--350
2003
341--350- 2002
1147.
Lin, C.; Heijmen, T.; Maten, J.; Kole, M.
ADAPT: Design assistance for iterative analogue synthesis
In W. Anheier and R. Laur and H. Gräb, Editor, Analog 2002 - Entwicklung von Analogschaltungen mit CAE-Methoden, BremenBand38ausGMM-Fachbericht, Seite 195-200
In W. Anheier and R. Laur and H. Gräb, Editor
Herausgeber: VDE Verlag GMBH, Berlin
Mai 20021146.
Klamroth, Kathrin; Wiecek, Margaret M.
A bi-objective median location problem with a line barrier
Operations Research, 50 :670-679
20021145.
Jacob, Birgit; Leblond, Juliette; Marmorat, Jean-Paul; Partington, Jonathan R.
A constrained approximation problem arising in parameter identification
, Band 351/352
Seite 487--500
2002
487--5001144.
Mannschreck, K.; B{ä}chmann, K.; Becker, Karl Heinz; Heil, Th.; Kurtenbach, Ralf; Memmesheimer, M.; Mohnen, V.; Obermeier, A.; Poppe, Dirk; Steinbrecher, R.; Schmitz, Th.; Volz-Thomas, A.; Zabel, Friedhelm
A database for volatile organic compounds
Journal of Atmospheric Chemistry, 42 (1-3) :281-286
2002
