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
- 1999
816.
Bunker, Philip R.; Jensen, Per
Spherical top molecules and the molecular symmetry group
Molecular Physics, 97 (1-2) :255-264
1999815.
Bunker, Philip R.; Jensen, Per
Spherical top molecules and the molecular symmetry group
Molecular Physics, 97 (1-2) :255-264
1999814.
Bunker, Philip R.; Jensen, Per
Spherical top molecules and the molecular symmetry group
Molecular Physics, 97 (1-2) :255-264
1999813.
Foster, Krishna L.; Caldwell, Tracy E.; Benter, Thorsten; Langer, Sarka; Hemminger, John C.; Finlayson-Pitts, Barbara J.
Techniques for quantifying gaseous HOCl using atmospheric pressure ionization mass spectrometry
Physical Chemistry Chemical Physics, 1 (24) :5615-5621
1999812.
Foster, Krishna L.; Caldwell, Tracy E.; Benter, Thorsten; Langer, Sarka; Hemminger, John C.; Finlayson-Pitts, Barbara J.
Techniques for quantifying gaseous HOCl using atmospheric pressure ionization mass spectrometry
Physical Chemistry Chemical Physics, 1 (24) :5615-5621
1999811.
Foster, Krishna L.; Caldwell, Tracy E.; Benter, Thorsten; Langer, Sarka; Hemminger, John C.; Finlayson-Pitts, Barbara J.
Techniques for quantifying gaseous HOCl using atmospheric pressure ionization mass spectrometry
Physical Chemistry Chemical Physics, 1 (24) :5615-5621
1999810.
Beutel, M.; Setzer, Klaus-Dieter; Fink, Ewald H.
The b\(^{1}\)\(\Sigma\)\(^{+}\)(b0\(^{+}\)) → X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{1}\)0\(^{+}\), X\(_{2}\)1) and a\(^{1}\)\(\Delta\)(a2) → X\(_{2}\)1 Transitions of AsI
Journal of Molecular Spectroscopy, 194 (2) :250-255
1999
Herausgeber: Academic Press809.
Beutel, M.; Setzer, Klaus-Dieter; Fink, Ewald H.
The b\(^{1}\)\(\Sigma\)\(^{+}\)(b0\(^{+}\)) → X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{1}\)0\(^{+}\), X\(_{2}\)1) and a\(^{1}\)\(\Delta\)(a2) → X\(_{2}\)1 Transitions of AsI
Journal of Molecular Spectroscopy, 194 (2) :250-255
1999
Herausgeber: Academic Press808.
Beutel, M.; Setzer, Klaus-Dieter; Fink, Ewald H.
The b\(^{1}\)\(\Sigma\)\(^{+}\)(b0\(^{+}\)) → X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{1}\)0\(^{+}\), X\(_{2}\)1) and a\(^{1}\)\(\Delta\)(a2) → X\(_{2}\)1 transitions of SbF, SbCl, SbBr, and SbI
Journal of Molecular Spectroscopy, 195 (1) :147-153
1999
Herausgeber: Academic Press807.
Beutel, M.; Setzer, Klaus-Dieter; Fink, Ewald H.
The b\(^{1}\)\(\Sigma\)\(^{+}\)(b0\(^{+}\)) → X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{1}\)0\(^{+}\), X\(_{2}\)1) and a\(^{1}\)\(\Delta\)(a2) → X\(_{2}\)1 transitions of SbF, SbCl, SbBr, and SbI
Journal of Molecular Spectroscopy, 195 (1) :147-153
1999
Herausgeber: Academic Press806.
Beutel, M.; Setzer, Klaus-Dieter; Fink, Ewald H.
The b1Σ+(b0+) → X3Σ-(X10+, X21) and a1Δ(a2) → X21 Transitions of AsI
Journal of Molecular Spectroscopy, 194 (2) :250-255
1999
Herausgeber: Academic Press805.
Beutel, M.; Setzer, Klaus-Dieter; Fink, Ewald H.
The b1Σ+(b0+) → X3Σ-(X10+, X21) and a1Δ(a2) → X21 transitions of SbF, SbCl, SbBr, and SbI
Journal of Molecular Spectroscopy, 195 (1) :147-153
1999
Herausgeber: Academic Press804.
Bunker, Philip R.; Bludsk{{\'y}}, Ota; Jensen, Per; Wesolowski, Steven S.; Van Huis, T. J.; Yamaguchi, Yukio; Schaefer, Henry F.
The H\(_{2}\)O\(^{++}\) Ground State Potential Energy Surface
Journal of Molecular Spectroscopy, 198 (2) :371-375
1999803.
Bunker, Philip R.; Bludsk{{\'y}}, Ota; Jensen, Per; Wesolowski, Steven S.; Van Huis, T. J.; Yamaguchi, Yukio; Schaefer, Henry F.
The H\(_{2}\)O\(^{++}\) Ground State Potential Energy Surface
Journal of Molecular Spectroscopy, 198 (2) :371-375
1999802.
Bunker, Philip R.; Bludský, Ota; Jensen, Per; Wesolowski, Steven S.; Van Huis, T. J.; Yamaguchi, Yukio; Schaefer, Henry F.
The H2O++ Ground State Potential Energy Surface
Journal of Molecular Spectroscopy, 198 (2) :371-375
1999801.
Becker, Karl Heinz; Freitas Dinis, Carlos M.; Geiger, Harald; Wiesen, Peter
The reactions of OH radicals with di-i-propoxymethane and di-sec-butoxymethane: Kinetic measurements and structure activity relationships
Physical Chemistry Chemical Physics, 1 (20) :4721-4726
1999800.
Becker, Karl Heinz; Freitas Dinis, Carlos M.; Geiger, Harald; Wiesen, Peter
The reactions of OH radicals with di-i-propoxymethane and di-sec-butoxymethane: Kinetic measurements and structure activity relationships
Physical Chemistry Chemical Physics, 1 (20) :4721-4726
1999799.
Becker, Karl Heinz; Freitas Dinis, Carlos M.; Geiger, Harald; Wiesen, Peter
The reactions of OH radicals with di-i-propoxymethane and di-sec-butoxymethane: Kinetic measurements and structure activity relationships
Physical Chemistry Chemical Physics, 1 (20) :4721-4726
1999798.
Gänsheimer, S; Schilling, A
Verbesserte prätherapeutische Abschätzung des pathologischen Tumorstadiums des Prostatakarzinoms anhand eines neuen Punktsystems
Aktuelle Urologie, 30 (01) :20--27
1999
Herausgeber: Georg Thieme Verlag Stuttgart{\textperiodcentered} New York797.
[german] Tausch, Michael W.; Schmidt, Andrea
β-Carotin - ein Multitalent
CHEMKON, 6 (3) :135--141
1999
Herausgeber: Wiley- 1998
796.
Tausch, Michael W.; Lowin, P.; Übel, M.
''Materialien-Manager Chemie'' Multimedia CD-ROM zur Erstellung von Arbeitsmaterialien für den Chemieunterricht
Herausgeber: C. C. Buchner, Bamberg
1998795.
Tausch, Michael W.; Wachtendonk, M.; Porth, H.-R.; Schulze, I.; Wambach, H.
''STOFF-FORMEL-UMWELT'', CHEMIE S I, 7. Schjg. in NRW
Herausgeber: C. C. Buchner, Bamberg
1998794.
Jacob, Birgit
A formula for the stability radius of time-varying systems
J. Differential Equations, 142 (1) :167--187
1998793.
Feldmann, Uwe
CAD-based electric-circuit modeling in industry II: Impact of circuit configurations and parameters
Surveys on Mathematics for Industry, 8 (2) :131--158
1998
Herausgeber: Wien; New York: Springer-Verlag, 1991-c2005.792.
Jacob, Birgit; Larsen, Mikael; Zwart, Hans
Corrections and extensions of: ``Optimal control of linear systems with almost periodic inputs" [SIAM J. Control Optim. \bf 25 (1987), no. 4, 1007--1019; MR0893995 (88i:93042)] by G. Da Prato and A. Ichikawa
SIAM J. Control Optim., 36 (4) :1473--1480
1998
