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
1179.
Günther, Michael; Arnold, Martin
Preconditioned splitting and overlapping techniques in modular time integration
4th MATHMOD Vienna. Proceedings IMACS Symposium on Mathematical ModellingausArgesim Report 24, Seite 1382–1387
Herausgeber: TU Wien
20031178.
Jankova, Katja; Hvilsted, S{\o}ren
Preparation of Poly(2,3,4,5,6-pentafluorostyrene) and Block Copolymers with Styrene by ATRP
Macromolecules, 36 (5) :1753--1758
2003
ISSN: 0024-92971177.
Sturm, Peter J.; Baltensperger, Urs; Bacher, Michael; Lechner, Bernhard; Hausberger, Stefan; Heiden, Bernhard; Imhof, David; Weingartner, Ernest; Pr{é}v{{\^o}}t, Andre S. H.; Kurtenbach, Ralf; Wiesen, Peter
Roadside measurements of particulate matter size distribution
, Atmospheric EnvironmentBand37, Seite 5273-5281
Herausgeber: Pergamon
20031176.
Sturm, Peter J.; Baltensperger, Urs; Bacher, Michael; Lechner, Bernhard; Hausberger, Stefan; Heiden, Bernhard; Imhof, David; Weingartner, Ernest; Pr{é}v{{\^o}}t, Andre S. H.; Kurtenbach, Ralf; Wiesen, Peter
Roadside measurements of particulate matter size distribution
, Atmospheric EnvironmentBand37, Seite 5273-5281
Herausgeber: Pergamon
20031175.
Sturm, Peter J.; Baltensperger, Urs; Bacher, Michael; Lechner, Bernhard; Hausberger, Stefan; Heiden, Bernhard; Imhof, David; Weingartner, Ernest; Prévôt, Andre S. H.; Kurtenbach, Ralf; Wiesen, Peter
Roadside measurements of particulate matter size distribution
, Atmospheric EnvironmentBand37, Seite 5273-5281
Herausgeber: Pergamon
20031174.
Heilmann, Margareta
Rodriguez-type representation for the eigenfunctions of Durrmeyer-type operators
Results in Mathematics, 44 (1-2) :97-105
20031173.
Lamour, R.; März, R.; Winkler, R.
Stability of periodic solutions of index-2 differential-algebraic systems
J. Math. Anal. Appl., 279 :475--494
20031172.
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, 1437-210X1171.
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, 1437-210X1170.
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
20031169.
Winkler, R.
Stochastic Differential Algebraic Equations of Index 1 and Applications in Circuit Simulation
J. Comp. Math. Appl., 157 :477--505
20031168.
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
20031167.
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 Press1166.
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 Press1165.
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 Press1164.
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 Press1163.
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 Press1162.
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 Press1161.
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
20031160.
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
20031159.
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
20031158.
Kirsch, Stefan; Bach, Thorsten
Total Synthesis of (+)-Wailupemycin B
Angewandte Chemie International Edition, 42 (38) :4685–4687
2003
ISSN: 1433-7851, 1521-37731157.
Kirsch, Stefan; Bach, Thorsten
Total Synthesis of (+)-Wailupemycin B
Angewandte Chemie International Edition, 42 (38) :4685–4687
2003
ISSN: 1433-7851, 1521-37731156.
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 Group1155.
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 Group
