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
- 1993
430.
Jensen, Per; Kozin, Igor N.
The Potential Energy Surface for the Electronic Ground State of H\(_{2}\)Se Derived from Experiment
Journal of Molecular Spectroscopy, 160 (1) :39-57
1993
Herausgeber: Academic Press429.
Jensen, Per; Kozin, Igor N.
The Potential Energy Surface for the Electronic Ground State of H\(_{2}\)Se Derived from Experiment
Journal of Molecular Spectroscopy, 160 (1) :39-57
1993
Herausgeber: Academic Press428.
Biggs, P.; Canosa-Mas, Carlos E.; Monks, P. S.; Wayne, Richard P.; Benter, Thorsten; Schindler, Ralph N.
The kinetics of the nitrate radical self-reaction
International Journal of Chemical Kinetics, 25 (10) :805-817
1993427.
Biggs, P.; Canosa-Mas, Carlos E.; Monks, P. S.; Wayne, Richard P.; Benter, Thorsten; Schindler, Ralph N.
The kinetics of the nitrate radical self-reaction
International Journal of Chemical Kinetics, 25 (10) :805-817
1993426.
Becker, Karl Heinz; Engelhardt, B.; Geiger, Harald; Kurtenbach, Ralf; Wiesen, Peter
Temperature dependence of the reactions of CH radicals with NO, NH\(_{3}\) and N\(_{2}\)O in the range 200-1300 K
Chemical Physics Letters, 210 (1-3) :135-140
1993425.
Kozin, Igor N.; Klee, Stefan; Jensen, Per; Polyansky, Oleg L.; Pavlichenkov, I. M.
The Far-Infrared Fourier Transform Spectrum of H2Se
Journal of Molecular Spectroscopy, 158 (2) :409-422
1993
Herausgeber: Academic Press424.
Kozin, Igor N.; Klee, Stefan; Jensen, Per; Polyansky, Oleg L.; Pavlichenkov, I. M.
The Far-Infrared Fourier Transform Spectrum of H\(_{2}\)Se
Journal of Molecular Spectroscopy, 158 (2) :409-422
1993
Herausgeber: Academic Press423.
Kozin, Igor N.; Klee, Stefan; Jensen, Per; Polyansky, Oleg L.; Pavlichenkov, I. M.
The Far-Infrared Fourier Transform Spectrum of H\(_{2}\)Se
Journal of Molecular Spectroscopy, 158 (2) :409-422
1993
Herausgeber: Academic Press422.
Jørgensen, Uffe G.; Jensen, Per
The Dipole Moment Surface and the Vibrational Transition Moments of H2O
Journal of Molecular Spectroscopy, 161 (1) :219-242
1993
Herausgeber: Academic Press421.
J{\o}rgensen, Uffe G.; Jensen, Per
The Dipole Moment Surface and the Vibrational Transition Moments of H\(_{2}\)O
Journal of Molecular Spectroscopy, 161 (1) :219-242
1993
Herausgeber: Academic Press420.
J{\o}rgensen, Uffe G.; Jensen, Per
The Dipole Moment Surface and the Vibrational Transition Moments of H\(_{2}\)O
Journal of Molecular Spectroscopy, 161 (1) :219-242
1993
Herausgeber: Academic Press419.
Shestakov, Oleg; Fink, Ewald H.
The a3Σ+(a11) - X1Σ+(X0+) transition of BiN
Chemical Physics Letters, 211 (4-5) :473-477
1993418.
Shestakov, Oleg; Fink, Ewald H.
The a\(^{3}\)\(\Sigma\)\(^{+}\)(a\(_{1}\)1) - X\(^{1}\)\(\Sigma\)\(^{+}\)(X0\(^{+}\)) transition of BiN
Chemical Physics Letters, 211 (4-5) :473-477
1993417.
Shestakov, Oleg; Fink, Ewald H.
The a\(^{3}\)\(\Sigma\)\(^{+}\)(a\(_{1}\)1) - X\(^{1}\)\(\Sigma\)\(^{+}\)(X0\(^{+}\)) transition of BiN
Chemical Physics Letters, 211 (4-5) :473-477
1993416.
Becker, Karl Heinz; Engelhardt, B.; Geiger, Harald; Kurtenbach, Ralf; Wiesen, Peter
Temperature dependence of the reactions of CH radicals with NO, NH3 and N2O in the range 200-1300 K
Chemical Physics Letters, 210 (1-3) :135-140
1993415.
Becker, Karl Heinz; Engelhardt, B.; Geiger, Harald; Kurtenbach, Ralf; Wiesen, Peter
Temperature dependence of the reactions of CH radicals with NO, NH\(_{3}\) and N\(_{2}\)O in the range 200-1300 K
Chemical Physics Letters, 210 (1-3) :135-140
1993414.
Denk, G.; G\"unther, Michael; Schmidt, W.
Olympische Chips: Schaltkreise -- Spannung in der Numerik
Technische Universit\"at M\"unchen, TUM-Sonderreihe Forschung f\"ur Bayern, Heft 6: Fakult\"at f\"ur Mathematik, Fakult\"at f\"ur Informatik, Seite 14--15
1993- 1992
413.
Heilmann, Margareta
Rate of approximation of weighted derivatives by linear combinations of SMD-operators
Numerical Methods in Approximation Theory - Proceedings of the conference held in Oberwolfach Germany, November 24-30, 1991, Seite 97-115
In D. Braess et al., Editor
Herausgeber: Birkhäuser, Basel, Int. Ser. Numer. Math. 105
1992412.
Bunker, Philip R.; Hamilton, I. P.; Jensen, Per
Rotation-vibration energies for the HO\(_{2}\) molecule
Journal of Molecular Spectroscopy, 155 (1) :44-54
1992411.
Becker, Karl Heinz; Engelhardt, B.; Geiger, Harald; Kurtenbach, Ralf; Schrey, G.; Wiesen, Peter
Temperature dependence of the CH+N2 reaction at low total pressure
Chemical Physics Letters, 195 (4) :322-328
1992410.
Shestakov, Oleg; Pravilov, A. M.; Demes, H.; Fink, Ewald H.
Radiative lifetime and quenching of the A \(^{2}\)\(\Sigma\)\(^{+}\) and X\(_{2}\) \(^{2}\)\(\Pi\)\(_{3/2}\) states of PbF
Chemical Physics, 165 (2-3) :415-427
1992409.
Shestakov, Oleg; Pravilov, A. M.; Demes, H.; Fink, Ewald H.
Radiative lifetime and quenching of the A 2Σ+ and X2 2Π3/2 states of PbF
Chemical Physics, 165 (2-3) :415-427
1992408.
Bunker, Philip R.; Hamilton, I. P.; Jensen, Per
Rotation-vibration energies for the HO\(_{2}\) molecule
Journal of Molecular Spectroscopy, 155 (1) :44-54
1992407.
Bunker, Philip R.; Hamilton, I. P.; Jensen, Per
Rotation-vibration energies for the HO2 molecule
Journal of Molecular Spectroscopy, 155 (1) :44-54
1992406.
Maten, E. J. W.; Melissen, J. B. M.
Simulation of inductive heating
{IEEE} Transactions on Magnetics, 28 (2) :1287--1290
März 1992
Herausgeber: Institute of Electrical and Electronics Engineers ({IEEE})
