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



1991

355.

Heilmann, Margareta; Müller, Manfred
Equivalence of a weighted modulus of smoothness and a modified weighted K-functional
In Nevai, P. and Pinkus, A., Editor
Herausgeber: Academic Press
1991

354.

Benter, Thorsten; Becker, Eilhard; Wille, Uta; Schindler, Ralph N.; Canosa-Mas, Carlos E.; Smith, Stuart J.; Waygood, Steven J.; Wayne, Richard P.
Nitrate radical reactions: interactions with alkynes
Journal of the Chemical Society, Faraday Transactions, 87 (14) :2141
1991

353.

Tausch, Michael W.
Legende oder nicht Legende?
Praxis der Naturwissenschaften (Chemie), 40 :44
1991

352.

Wildt, Jürgen; Bednarek, G.; Fink, Ewald H.; Wayne, Richard P.
Laser excitation of the A3Σu+, A'3Δu and c1Σu- states of molecular oxygen
Chemical Physics, 156 (3) :497-508
1991

351.

Wildt, J{ü}rgen; Bednarek, G.; Fink, Ewald H.; Wayne, Richard P.
Laser excitation of the A\(^{3}\)\(\Sigma\)\(_{u}\)\(^{+}\), A'\(^{3}\)\(\Delta\)\(_{u}\) and c\(^{1}\)\(\Sigma\)\(_{u}\)\(^{-}\) states of molecular oxygen
Chemical Physics, 156 (3) :497-508
1991

350.

Wildt, J{ü}rgen; Bednarek, G.; Fink, Ewald H.; Wayne, Richard P.
Laser excitation of the A\(^{3}\)\(\Sigma\)\(_{u}\)\(^{+}\), A'\(^{3}\)\(\Delta\)\(_{u}\) and c\(^{1}\)\(\Sigma\)\(_{u}\)\(^{-}\) states of molecular oxygen
Chemical Physics, 156 (3) :497-508
1991

349.

Becker, Karl Heinz; Geiger, Harald; Wiesen, Peter
Kinetic study of the OH radical chain in the reaction system OH + C2H4 + NO + air
Chemical Physics Letters, 184 (4) :256-261
1991

348.

Becker, Karl Heinz; Geiger, Harald; Wiesen, Peter
Kinetic study of the OH radical chain in the reaction system OH + C\(_{2}\)H\(_{4}\) + NO + air
Chemical Physics Letters, 184 (4) :256-261
1991

347.

Becker, Karl Heinz; Geiger, Harald; Wiesen, Peter
Kinetic study of the OH radical chain in the reaction system OH + C\(_{2}\)H\(_{4}\) + NO + air
Chemical Physics Letters, 184 (4) :256-261
1991

346.

Jensen, Per; Oddershede, Jens; Sabin, John R.
Geometric dependence of the mean excitation energy and spectral moments of water
Physical Review A, 43 (7) :4040-4043
1991

345.

Jensen, Per; Oddershede, Jens; Sabin, John R.
Geometric dependence of the mean excitation energy and spectral moments of water
Physical Review A, 43 (7) :4040-4043
1991

344.

Jensen, Per; Oddershede, Jens; Sabin, John R.
Geometric dependence of the mean excitation energy and spectral moments of water
Physical Review A, 43 (7) :4040-4043
1991

343.

Vilesov, A. F.; Wildt, Jürgen; Fink, Ewald H.
Emission of Xe: N(2P) collision complexes near the N(2P→2D) lines
Chemical Physics, 153 (3) :531-537
1991

342.

Benter, Thorsten; Becker, Eilhard; Wille, Uta; Schindler, Ralph N.; Canosa-Mas, Carlos E.; Smith, Stuart J.; Waygood, Steven J.; Wayne, Richard P.
Nitrate radical reactions: interactions with alkynes
Journal of the Chemical Society, Faraday Transactions, 87 (14) :2141
1991

341.

Vilesov, A. F.; Wildt, J{ü}rgen; Fink, Ewald H.
Emission of Xe: N(\(^{2}\)P) collision complexes near the N(\(^{2}\)P→\(^{2}\)D) lines
Chemical Physics, 153 (3) :531-537
1991

340.

Vilesov, A. F.; Wildt, J{ü}rgen; Fink, Ewald H.
Emission of Xe: N(\(^{2}\)P) collision complexes near the N(\(^{2}\)P→\(^{2}\)D) lines
Chemical Physics, 153 (3) :531-537
1991

339.

Fink, Ewald H.; Setzer, Klaus-Dieter; Wildt, Jürgen; Ramsay, D. A.; Vervloet, M.
Collision-induced emission of O2(b1Σg+ → a1Δg) in the gas phase
International Journal of Quantum Chemistry, 39 (3) :287-298
1991

338.

Fink, Ewald H.; Setzer, Klaus-Dieter; Wildt, J{ü}rgen; Ramsay, D. A.; Vervloet, M.
Collision-induced emission of O\(_{2}\)(b\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → a\(^{1}\)\(\Delta\)\(_{g}\)) in the gas phase
International Journal of Quantum Chemistry, 39 (3) :287-298
1991

337.

Fink, Ewald H.; Setzer, Klaus-Dieter; Wildt, J{ü}rgen; Ramsay, D. A.; Vervloet, M.
Collision-induced emission of O\(_{2}\)(b\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → a\(^{1}\)\(\Delta\)\(_{g}\)) in the gas phase
International Journal of Quantum Chemistry, 39 (3) :287-298
1991

336.

Bunker, Philip R.; Epa, V. C.; Jensen, Per; Karpfen, Alfred
An analytical ab initio potential surface and the calculated tunneling energies for the HCl dimer
Journal of Molecular Spectroscopy, 146 (1) :200-219
1991

335.

Bunker, Philip R.; Epa, V. C.; Jensen, Per; Karpfen, Alfred
An analytical ab initio potential surface and the calculated tunneling energies for the HCl dimer
Journal of Molecular Spectroscopy, 146 (1) :200-219
1991

334.

Bunker, Philip R.; Epa, V. C.; Jensen, Per; Karpfen, Alfred
An analytical ab initio potential surface and the calculated tunneling energies for the HCl dimer
Journal of Molecular Spectroscopy, 146 (1) :200-219
1991

333.

Karpfen, Alfred; Bunker, Philip R.; Jensen, Per
An ab initio study of the hydrogen chloride dimer: the potential energy surface and the characterization of the stationary points
Chemical Physics, 149 (3) :299-309
1991

332.

Karpfen, Alfred; Bunker, Philip R.; Jensen, Per
An ab initio study of the hydrogen chloride dimer: the potential energy surface and the characterization of the stationary points
Chemical Physics, 149 (3) :299-309
1991

331.

Karpfen, Alfred; Bunker, Philip R.; Jensen, Per
An ab initio study of the hydrogen chloride dimer: the potential energy surface and the characterization of the stationary points
Chemical Physics, 149 (3) :299-309
1991

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