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



1996

642.

G\"unther, Michael; Rentrop, P.
The {NAND-gate} -- a benchmark for the numerical simulation of digital circuits
In W.~Mathis and P.~Noll, Editor, 2.ITG-Diskussionssitzung ''Neue Anwendungen Theoretischer Konzepte in der Elektrotechnik - mit Gedenksitzung zum 50. Todestag von Wilhelm Cauer'', Seite 27--33
In W.~Mathis and P.~Noll, Editor
Herausgeber: Berlin, VDE-Verlag
1996

641.

Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\) → X\(^{3}\)\(\Sigma\)\(^{-}\) Transitions of AsH and AsD
Journal of Molecular Spectroscopy, 178 (2) :165-171
1996
Herausgeber: Academic Press

640.

Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\) → X\(^{3}\)\(\Sigma\)\(^{-}\) Transitions of AsH and AsD
Journal of Molecular Spectroscopy, 178 (2) :165-171
1996
Herausgeber: Academic Press

639.

Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\) → X\(^{3}\)\(\Sigma\)\(^{-}\) transitions of PH and PD
Chemical Physics Letters, 249 (3-4) :183-190
1996

638.

Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\) → X\(^{3}\)\(\Sigma\)\(^{-}\) transitions of PH and PD
Chemical Physics Letters, 249 (3-4) :183-190
1996

637.

Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\)(a2) → X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{2}\)1) Transitions of SbH and SbD
Journal of Molecular Spectroscopy, 179 (1) :79-84
1996
Herausgeber: Academic Press

636.

Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\)(a2) → X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{2}\)1) Transitions of SbH and SbD
Journal of Molecular Spectroscopy, 179 (1) :79-84
1996
Herausgeber: Academic Press

635.

Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\)(a2) States of BiCl, BiBr, and BiI
Journal of Molecular Spectroscopy, 175 (1) :48-53
1996
Herausgeber: Academic Press

634.

Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a\(^{1}\)\(\Delta\)(a2) States of BiCl, BiBr, and BiI
Journal of Molecular Spectroscopy, 175 (1) :48-53
1996
Herausgeber: Academic Press

633.

Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a1Δ → X3Σ- Transitions of AsH and AsD
Journal of Molecular Spectroscopy, 178 (2) :165-171
1996
Herausgeber: Academic Press

632.

Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a1Δ → X3Σ- transitions of PH and PD
Chemical Physics Letters, 249 (3-4) :183-190
1996

631.

Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a1Δ(a2) → X3Σ-(X21) Transitions of SbH and SbD
Journal of Molecular Spectroscopy, 179 (1) :79-84
1996
Herausgeber: Academic Press

630.

Beutel, M.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
The a1Δ(a2) States of BiCl, BiBr, and BiI
Journal of Molecular Spectroscopy, 175 (1) :48-53
1996
Herausgeber: Academic Press

629.

Günther, Michael; Rentrop, Peter
The differential-algebraic index concept in electric circuit simulation
, Proceedings of the 3rd International Congress on Industrial and Applied MathematicsBand76, Seite 91–94
Herausgeber: Akademie Verlag Berlin
1996

628.


The differential-algebraic index concept in electric circuit simulation
Zeitschrift fur angewandte Mathematik und Mechanik, 76 (1) :91--94
1996

627.

Denk, Georg; Günther, Michael
The influence of MOSFET model and network equations on circuit simulation
Preprint (1842)
1996
Herausgeber: Technische Hochschule Darmstadt

626.

Polyansky, Oleg L.; Jensen, Per; Tennyson, Jonathan
The potential energy surface of H\(_{2}\)\(^{16}\)O
Journal of Chemical Physics, 105 (15) :6490-6497
1996

625.

Polyansky, Oleg L.; Jensen, Per; Tennyson, Jonathan
The potential energy surface of H\(_{2}\)\(^{16}\)O
Journal of Chemical Physics, 105 (15) :6490-6497
1996

624.

Polyansky, Oleg L.; Jensen, Per; Tennyson, Jonathan
The potential energy surface of H216O
Journal of Chemical Physics, 105 (15) :6490-6497
1996

623.

Polyansky, Oleg L.; Jensen, Per; Tennyson, Jonathan
The Potential Energy Surface of Hydrogen Sulfide
Journal of Molecular Spectroscopy, 178 (2) :184-188
1996
Herausgeber: Academic Press

622.

Polyansky, Oleg L.; Jensen, Per; Tennyson, Jonathan
The Potential Energy Surface of Hydrogen Sulfide
Journal of Molecular Spectroscopy, 178 (2) :184-188
1996
Herausgeber: Academic Press

621.

Polyansky, Oleg L.; Jensen, Per; Tennyson, Jonathan
The Potential Energy Surface of Hydrogen Sulfide
Journal of Molecular Spectroscopy, 178 (2) :184-188
1996
Herausgeber: Academic Press

620.

Kozin, Igor N.; Jensen, Per; Polanz, Oliver; Klee, Stefan; Poteau, Laurent; Demaison, Jean
The Rotational Spectrum of H\(_{2}\)Te
Journal of Molecular Spectroscopy, 180 (2) :402-413
1996
Herausgeber: Academic Press

619.

Kozin, Igor N.; Jensen, Per; Polanz, Oliver; Klee, Stefan; Poteau, Laurent; Demaison, Jean
The Rotational Spectrum of H\(_{2}\)Te
Journal of Molecular Spectroscopy, 180 (2) :402-413
1996
Herausgeber: Academic Press

618.

Kozin, Igor N.; Jensen, Per; Polanz, Oliver; Klee, Stefan; Poteau, Laurent; Demaison, Jean
The Rotational Spectrum of H2Te
Journal of Molecular Spectroscopy, 180 (2) :402-413
1996
Herausgeber: Academic Press