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



1997

704.

Becker, Karl Heinz; Kurtenbach, Ralf; Schmidt, Frank; Wiesen, Peter
Kinetics of the Reactions of NCO Radicals with NO and NH\(_{3}\)
Berichte der Bunsengesellschaft für physikalische Chemie, 101 (1) :128-133
1997

703.

Becker, Karl Heinz; Kurtenbach, Ralf; Schmidt, Frank; Wiesen, Peter
Kinetics of the Reactions of NCO Radicals with NO and NH3
Berichte der Bunsengesellschaft für physikalische Chemie, 101 (1) :128-133
1997

702.

Tausch, Michael W.; Brandl, H.
Lichtbeteiligung bei chemischen Reaktionen
MNU, 50 :206
1997

701.

Günther, Michael
Modelling transmission lines effects in integrated circuits by a mixed system of DAEs and PDEs
In Troch, I. and Breitenecker, F., Editor, 2nd MATHMOD Vienna. Proceedings IMACS Symposium on Mathematical ModellingBand11ausArgesim Report 15, Seite 535–540
In Troch, I. and Breitenecker, F., Editor
Herausgeber: TU Wien
1997

700.

Ehrgott, Matthias; Klamroth, Kathrin
Nonconnected efficiency graphs in multiple criteria combinatorial optimization
In Caballero, R. and Ruiz, F. and Steuer, R.E., Editor, Advances in Multiple Objective and Goal ProgrammingBand455ausLecture Notes in Economics and Mathematical Systems, Seite 140-150
In Caballero, R. and Ruiz, F. and Steuer, R.E., Editor
1997

699.

Günther, Michael; Ostermann, Alexander
Numerical treatment of ordinary and algebra-differential equations
Preprint (1934)
1997
Herausgeber: Technische Hochschule Darmstadt

698.

Schryber, Jeremy H.; Polyansky, Oleg L.; Jensen, Per; Tennyson, Jonathan
On the spectroscopically determined potential energy surfaces for the electronic ground states of NO\(_{2}\) and H\(_{2}\)O
Journal of Molecular Spectroscopy, 185 (2) :234-243
1997
Herausgeber: Academic Press

697.

Schryber, Jeremy H.; Polyansky, Oleg L.; Jensen, Per; Tennyson, Jonathan
On the spectroscopically determined potential energy surfaces for the electronic ground states of NO\(_{2}\) and H\(_{2}\)O
Journal of Molecular Spectroscopy, 185 (2) :234-243
1997
Herausgeber: Academic Press

696.

Schryber, Jeremy H.; Polyansky, Oleg L.; Jensen, Per; Tennyson, Jonathan
On the spectroscopically determined potential energy surfaces for the electronic ground states of NO2 and H2O
Journal of Molecular Spectroscopy, 185 (2) :234-243
1997
Herausgeber: Academic Press

695.

Günther, M.; Hoschek, M.
ROW methods adapted to electric circuit simulation packages
Journal of Computational and Applied Mathematics, 82 (1) :159–170
1997
Herausgeber: Elsevier

694.

Günther, Michael; Hoschek, Markus
ROW methods adapted to electric circuit simulation packages
Journal of computational and applied mathematics, 82 (1-2) :159--170
1997
Herausgeber: North-Holland

693.

Tausch, Michael W.
Simulation von chemischen Gleichgewichten
Computer + Unterricht, 26 :35
1997

692.

Bludsky, Ota; Jensen, Per
The calculation of the bound and quasibound vibrational states for ozone in its \(^{1}\)B\(_{2}\) electronic state
Molecular Physics, 91 (4) :653-662
1997

691.

Bludsky, Ota; Jensen, Per
The calculation of the bound and quasibound vibrational states for ozone in its \(^{1}\)B\(_{2}\) electronic state
Molecular Physics, 91 (4) :653-662
1997

690.

Bludsky, Ota; Jensen, Per
The calculation of the bound and quasibound vibrational states for ozone in its 1B2 electronic state
Molecular Physics, 91 (4) :653-662
1997

689.

Kozin, Igor N.; Jensen, Per
The Effects of Nonzero Total Electron Spin in the X\verb=~= \(^{3}\)B\(_{1}\) State of Methylene CH\(_{2}\)
Journal of Molecular Spectroscopy, 183 (2) :398-406
1997
Herausgeber: Academic Press

688.

Kozin, Igor N.; Jensen, Per
The Effects of Nonzero Total Electron Spin in the X\verb=~= \(^{3}\)B\(_{1}\) State of Methylene CH\(_{2}\)
Journal of Molecular Spectroscopy, 183 (2) :398-406
1997
Herausgeber: Academic Press

687.

Kozin, Igor N.; Jensen, Per
The Effects of Nonzero Total Electron Spin in the X~ 3B1 State of Methylene CH2
Journal of Molecular Spectroscopy, 183 (2) :398-406
1997
Herausgeber: Academic Press

686.

Klamroth, Kathrin; Mengersen, Ingrid
The Ramsey number r(K_1,3,C_4,K_4)
Utilitas Mathematica, 52 :65-81
1997

685.

Jensen, Per; Sauer, Stephan P. A.
Theoretical calculations of the hyperfine structure in the spectra of H\(_{3}\)\(^{+}\) and its deuterated isotopomers
Molecular Physics, 91 (2) :319-332
1997

684.

Jensen, Per; Sauer, Stephan P. A.
Theoretical calculations of the hyperfine structure in the spectra of H\(_{3}\)\(^{+}\) and its deuterated isotopomers
Molecular Physics, 91 (2) :319-332
1997

683.

Jensen, Per; Sauer, Stephan P. A.
Theoretical calculations of the hyperfine structure in the spectra of H3+ and its deuterated isotopomers
Molecular Physics, 91 (2) :319-332
1997

682.

Jensen, Per
Theoretical Rotation-Vibration Energies of X\verb=~=\(^{3}\)B\(_{1}\) NH\(_{2}\)\(^{+}\)
Journal of Molecular Spectroscopy, 181 (1) :207-214
1997
Herausgeber: Academic Press

681.

Jensen, Per
Theoretical Rotation-Vibration Energies of X\verb=~=\(^{3}\)B\(_{1}\) NH\(_{2}\)\(^{+}\)
Journal of Molecular Spectroscopy, 181 (1) :207-214
1997
Herausgeber: Academic Press

680.

Jensen, Per
Theoretical Rotation-Vibration Energies of X~3B1 NH2+
Journal of Molecular Spectroscopy, 181 (1) :207-214
1997
Herausgeber: Academic Press