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
495.
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
1994479.
Tashkun, Sergey A.; Jensen, Per
The low-energy part of the potential function for the electronic ground state of NO\(_{2}\) derived from experiment
Journal of Molecular Spectroscopy, 165 (1) :173-184
1994
Herausgeber: Academic Press478.
Tashkun, Sergey A.; Jensen, Per
The low-energy part of the potential function for the electronic ground state of NO\(_{2}\) derived from experiment
Journal of Molecular Spectroscopy, 165 (1) :173-184
1994
Herausgeber: Academic Press477.
Tashkun, Sergey A.; Jensen, Per
The low-energy part of the potential function for the electronic ground state of NO2 derived from experiment
Journal of Molecular Spectroscopy, 165 (1) :173-184
1994
Herausgeber: Academic Press476.
Jensen, Per; Bunker, Philip R.
The Molecular Symmetry Group for Molecules in High Angular Momentum States
Journal of Molecular Spectroscopy, 164 (1) :315-317
1994
Herausgeber: Academic Press475.
Jensen, Per; Bunker, Philip R.
The Molecular Symmetry Group for Molecules in High Angular Momentum States
Journal of Molecular Spectroscopy, 164 (1) :315-317
1994
Herausgeber: Academic Press474.
Jensen, Per; Bunker, Philip R.
The Molecular Symmetry Group for Molecules in High Angular Momentum States
Journal of Molecular Spectroscopy, 164 (1) :315-317
1994
Herausgeber: Academic Press473.
Bednarek, G.; Wayne, R.P.; Wildt, J{ü}rgen; Fink, E.H.
The yield of O\(_{2}\)(b \(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\), v=0) produced by quenching of O\(_{2}\)(A \(^{3}\)\(\Sigma\)\(_{u}\)\(^{+}\), v=8) by O\(_{2}\)
Chemical Physics, 185 (2) :251-261
1994472.
Bednarek, G.; Wayne, R.P.; Wildt, J{ü}rgen; Fink, E.H.
The yield of O\(_{2}\)(b \(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\), v=0) produced by quenching of O\(_{2}\)(A \(^{3}\)\(\Sigma\)\(_{u}\)\(^{+}\), v=8) by O\(_{2}\)
Chemical Physics, 185 (2) :251-261
1994471.
Bednarek, G.; Wayne, R.P.; Wildt, Jürgen; Fink, E.H.
The yield of O2(b 1Σg+, v=0) produced by quenching of O2(A 3Σu+, v=8) by O2
Chemical Physics, 185 (2) :251-261
1994
