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
- 1994
504.
[german] Tausch, Michael W.
Ozon - Unterrichtsmaterialien für die S II
Praxis der Naturwissenschaften (Chemie), 43 (4) :27
1994503.
Gerstberger, Robert; Günther, Michael
Parallelization of a charge-oriented extrapolation method on the SNI-KSR1
Overview of Research on the Parallel Computer SNI-KSR at the Leibniz-Rechenzentrum Miinchen, 9401 :57--61
1994
Herausgeber: M\"unchen, LRZ502.
Günther, Michael; Rentrop, Peter
Partitioning and multirate strategies in latent electric circuits
In Bank, R. E. and Gajewski, H. and Bulirsch, R. and Merten, K., Editor, Mathematical modelling and simulation of electrical circuits and semiconductor devicesausISNM International Series of Numerical Mathematics, Seite 33–60
In Bank, R. E. and Gajewski, H. and Bulirsch, R. and Merten, K., Editor
Herausgeber: Birkhäuser Basel
1994501.
[german] Tausch, Michael W.
Photo-Blue-Bottle Modellversuche zur Photosynthese und zur Atmung
Praxis der Naturwissenschaften (Chemie), 43 (3) :13
1994500.
Klamroth, Kathrin
Ramsey-Zahlen für Mengen von Graphen
Technical University of Braunschweig
1994499.
Benter, Thorsten; Liesner, M.; Schindler, Ralph N.; Skov, H.; Hjorth, J.; Restelli, G.
REMPI-MS and FTIR Study of NO\(_{2}\) and Oxirane Formation in the Reactions of Unsaturated Hydrocarbons with NO\(_{3}\) Radicals
The Journal of Physical Chemistry, 98 (41) :10492-10496
1994498.
Benter, Thorsten; Liesner, M.; Schindler, Ralph N.; Skov, H.; Hjorth, J.; Restelli, G.
REMPI-MS and FTIR Study of NO\(_{2}\) and Oxirane Formation in the Reactions of Unsaturated Hydrocarbons with NO\(_{3}\) Radicals
The Journal of Physical Chemistry, 98 (41) :10492-10496
1994497.
Benter, Thorsten; Liesner, M.; Schindler, Ralph N.; Skov, H.; Hjorth, J.; Restelli, G.
REMPI-MS and FTIR Study of NO2 and Oxirane Formation in the Reactions of Unsaturated Hydrocarbons with NO3 Radicals
The Journal of Physical Chemistry, 98 (41) :10492-10496
1994496.
KIELAU, G; Maißer, P
SIMULATION OF BOBSLED RUNS-PAPER PRESENTED AT THE GAMM ANNUAL-MEETING IN DRESDEN, APRIL 12-16, 1993
1994495.
Kielau, Gerald; Maißer, P
Simulation von Fahren gesteuerter Bobschlitten
Zeitschrift für angewandte Mathematik und Mechanik, 74 (9) :434--435
1994494.
Günther, Michael; Rentrop, Peter
Suitable one-step methods for quasilinear-implicit ode's
Herausgeber: Mathematisches Institut und Institut für Informatik der Technischen~…
1994493.
Auwera, J. Vander; Holland, J. K.; Jensen, Per; Johns, John W. C.
The \(\nu\)\(_{6}\) band system of C\(_{3}\)O\(_{2}\) near 540 cm\(^{-1}\)
Journal of Molecular Spectroscopy, 163 (2) :529-540
1994
Herausgeber: Academic Press492.
Auwera, J. Vander; Holland, J. K.; Jensen, Per; Johns, John W. C.
The \(\nu\)\(_{6}\) band system of C\(_{3}\)O\(_{2}\) near 540 cm\(^{-1}\)
Journal of Molecular Spectroscopy, 163 (2) :529-540
1994
Herausgeber: Academic Press491.
Breidohr, R.; Shestakov, Oleg; Fink, Ewald H.
The a \(^{3}\)\(\Sigma\)\(^{+}\) (a\(_{1}\) 1) → X \(^{1}\)\(\Sigma\)\(^{+}\) (X 0\(^{+}\)) Transitions of BiP, BiAs, and BiSb
Journal of Molecular Spectroscopy, 168 (1) :126-135
1994
Herausgeber: Academic Press490.
Breidohr, R.; Shestakov, Oleg; Fink, Ewald H.
The a \(^{3}\)\(\Sigma\)\(^{+}\) (a\(_{1}\) 1) → X \(^{1}\)\(\Sigma\)\(^{+}\) (X 0\(^{+}\)) Transitions of BiP, BiAs, and BiSb
Journal of Molecular Spectroscopy, 168 (1) :126-135
1994
Herausgeber: Academic Press489.
Breidohr, R.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.; Zyrnicki, W.
The a \(^{3}\)\(\Sigma\)\(_{u}\)\(^{+}\) (a\(_{1}\) 1\(_{u}\)) → X \(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) (X 0\(_{g}\)\(^{+}\)) Transition of Bi\(_{2}\)
Journal of Molecular Spectroscopy, 166 (2) :251-263
1994
Herausgeber: Academic Press488.
Breidohr, R.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.; Zyrnicki, W.
The a \(^{3}\)\(\Sigma\)\(_{u}\)\(^{+}\) (a\(_{1}\) 1\(_{u}\)) → X \(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) (X 0\(_{g}\)\(^{+}\)) Transition of Bi\(_{2}\)
Journal of Molecular Spectroscopy, 166 (2) :251-263
1994
Herausgeber: Academic Press487.
Breidohr, R.; Shestakov, Oleg; Fink, Ewald H.
The a \(^{3}\)\(\Sigma\)\(_{u}\)\(^{+}\)(a\(_{1}\) 1\(_{u}\)) → X \(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) (X 0\(_{g}\)\(^{+}\)) transition of Sb\(_{2}\)
Chemical Physics Letters, 218 (1-2) :13-16
1994486.
Breidohr, R.; Shestakov, Oleg; Fink, Ewald H.
The a \(^{3}\)\(\Sigma\)\(_{u}\)\(^{+}\)(a\(_{1}\) 1\(_{u}\)) → X \(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) (X 0\(_{g}\)\(^{+}\)) transition of Sb\(_{2}\)
Chemical Physics Letters, 218 (1-2) :13-16
1994485.
Breidohr, R.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.; Zyrnicki, W.
The a 3Σu+ (a1 1u) → X 1Σg+ (X 0g+) Transition of Bi2
Journal of Molecular Spectroscopy, 166 (2) :251-263
1994
Herausgeber: Academic Press484.
Breidohr, R.; Shestakov, Oleg; Fink, Ewald H.
The a 3Σu+(a1 1u) → X 1Σg+ (X 0g+) transition of Sb2
Chemical Physics Letters, 218 (1-2) :13-16
1994483.
Breidohr, R.; Shestakov, Oleg; Fink, Ewald H.
The a 3Σ+ (a1 1) → X 1Σ+ (X 0+) Transitions of BiP, BiAs, and BiSb
Journal of Molecular Spectroscopy, 168 (1) :126-135
1994
Herausgeber: Academic Press482.
Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\)(a2) state of BiF
Chemical Physics Letters, 229 (3) :273-278
1994481.
Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\)(a2) state of BiF
Chemical Physics Letters, 229 (3) :273-278
1994480.
Shestakov, Oleg; Fink, Ewald H.
The a1Δ(a2) state of BiF
Chemical Physics Letters, 229 (3) :273-278
1994
