Applied and Computational Mathematics (ACM)

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

453.

G\"unther, Michael; Rentrop, P.
Multirate {ROW} methods and latency of electric circuits
Appl.~Numer.~Math., 13 :83--102
1993

452.

Günther, Michael; Rentrop, Peter
Multirate ROW methods and latency of electric circuits
Applied Numerical Mathematics, 13 (1) :83–102
1993
Herausgeber: Elsevier

DOI: 10.1016/0168-9274(93)90133-C

451.

Günther, Michael; Rentrop, Peter
Multirate ROW methods and latency of electric circuits
Applied Numerical Mathematics, 13 (1-3) :83--102
1993
Herausgeber: North-Holland

450.

Denk, G.; Günther, M.; Schmidt, W.
Olympische Chips: Schaltkreise - Spannung in der Numerik
1993

449.

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

448.

[german] Tausch, Michael W.; Kolkowski, M.; Weilert, K.
Ozon - der andere Sauerstoff
Praxis der Naturwissenschaften (Chemie), 42 (1) :26
1993

447.

Günther, Michael; Rentrop, Peter
Partitioning and multirate strategies in latent electric circuits
1993

446.

Shestakov, Oleg; Demes, H.; Fink, Ewald H.
Radiative lifetimes of the A \(^{2}\)\(\Sigma\)\(_{1/2}\)\(^{+}\) and X\(_{2}\) \(^{2}\)\(\Pi\)\(_{3/2}\) states of lead monohalides
Chemical Physics, 178 (1-3) :561-567
1993

DOI: 10.1016/0301-0104(93)85092-M

445.

Shestakov, Oleg; Demes, H.; Fink, Ewald H.
Radiative lifetimes of the A \(^{2}\)\(\Sigma\)\(_{1/2}\)\(^{+}\) and X\(_{2}\) \(^{2}\)\(\Pi\)\(_{3/2}\) states of lead monohalides
Chemical Physics, 178 (1-3) :561-567
1993

DOI: 10.1016/0301-0104(93)85092-M

444.

Shestakov, Oleg; Demes, H.; Fink, Ewald H.
Radiative lifetimes of the A 2Σ1/2+ and X2 2Π3/2 states of lead monohalides
Chemical Physics, 178 (1-3) :561-567
1993

DOI: 10.1016/0301-0104(93)85092-M

443.

Schilders, W. H. A.; Maten, E. J. W.; Rusch, J. J.; Heynderickx, I. E. J.
Simulation of non-isothermal Couette flow of liquid crystalline polymers
In Taylor, C., Editor, Numerical methods in laminar and turbulent flowBand8(1), Seite 480-491
In Taylor, C., Editor
Herausgeber: Pineridge Press Lmt, Swansea, UK
1993

442.

Maten, E. J. W.
Simulation of radiation heat transfer in television tubes
In R. W. Lewis, Editor, Numerical methods in thermal problemsBand8(1), Seite 831-842
In R. W. Lewis, Editor
Herausgeber: Pineridge Press Lmt, Swansea, UK
1993

441.

Maten, E. J. W.; Heynderickx, I. E. J.; Potze, W.; Rusch, J. J.; Schilders, W. H. A.
Simulation of steady non-isothermal flow of liquid crystalline polymers
In K. Morgan and E. Onate and J. Periaux and J. Peraire and O. C. Zienkiewicz, Editor, Finite elements in fluids, New trends and applicationsBand1, Seite 572-581
In K. Morgan and E. Onate and J. Periaux and J. Peraire and O. C. Zienkiewicz, Editor
Herausgeber: Centro Int. de Metodos Num. en Ing. (CIMNE), Barcelona and Pineridge Press Lmt, Swansea, UK
1993

440.

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
1993

DOI: 10.1016/0009-2614(93)89113-V

439.

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
1993

DOI: 10.1016/0009-2614(93)89113-V

438.

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
1993

DOI: 10.1016/0009-2614(93)89113-V

437.

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
1993

DOI: 10.1016/0009-2614(93)87093-I

436.

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
1993

DOI: 10.1016/0009-2614(93)87093-I

435.

Shestakov, Oleg; Fink, Ewald H.
The a3Σ+(a11) - X1Σ+(X0+) transition of BiN
Chemical Physics Letters, 211 (4-5) :473-477
1993

DOI: 10.1016/0009-2614(93)87093-I

434.

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 Press

DOI: 10.1006/JMSP.1993.1228

433.

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 Press

DOI: 10.1006/JMSP.1993.1228

432.

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 Press

DOI: 10.1006/JMSP.1993.1228

431.

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 Press

DOI: 10.1006/JMSP.1993.1085

430.

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 Press

DOI: 10.1006/JMSP.1993.1085

429.

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 Press

DOI: 10.1006/JMSP.1993.1085