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



1998

787.

Tausch, Michael W.; Grolmuss, A.; Piwek, B.
Echtfarben-Emissionsspektren EFES - Ein Beitrag zum Verständnis von Licht und Farbe
Praxis der Naturwissenschaften (Chemie), 47 (2) :10
1998

786.

Shestakov, Oleg; Breidohr, R.; Demes, H.; Setzer, Klaus-Dieter; Fink, Ewald H.
Electronic States and Spectra of BiO
Journal of Molecular Spectroscopy, 190 (1) :28-77
1998
Herausgeber: Academic Press

785.

Shestakov, Oleg; Breidohr, R.; Demes, H.; Setzer, Klaus-Dieter; Fink, Ewald H.
Electronic States and Spectra of BiO
Journal of Molecular Spectroscopy, 190 (1) :28-77
1998
Herausgeber: Academic Press

784.

Shestakov, Oleg; Breidohr, R.; Demes, H.; Setzer, Klaus-Dieter; Fink, Ewald H.
Electronic States and Spectra of BiO
Journal of Molecular Spectroscopy, 190 (1) :28-77
1998
Herausgeber: Academic Press

783.

Brasseur, G. P.; Cox, R. A.; Hauglustaine, D.; Isaksen, I.; Lelieveld, J.; Lister, D. H.; Sausen, R.; Schumann, Ulrich; Wahner, A.; Wiesen, Peter
European scientific assessment of the atmospheric effects of aircraft emissions
Atmospheric Environment, 32 (13) :2329-2418
1998

782.

Brasseur, G. P.; Cox, R. A.; Hauglustaine, D.; Isaksen, I.; Lelieveld, J.; Lister, D. H.; Sausen, R.; Schumann, Ulrich; Wahner, A.; Wiesen, Peter
European scientific assessment of the atmospheric effects of aircraft emissions
Atmospheric Environment, 32 (13) :2329-2418
1998

781.

Brasseur, G. P.; Cox, R. A.; Hauglustaine, D.; Isaksen, I.; Lelieveld, J.; Lister, D. H.; Sausen, R.; Schumann, Ulrich; Wahner, A.; Wiesen, Peter
European scientific assessment of the atmospheric effects of aircraft emissions
Atmospheric Environment, 32 (13) :2329-2418
1998

780.

Shestakov, Oleg; Gielen, R.; Setzer, Klaus-Dieter; Fink, Ewald H.
Gas phase LIF study of the b\(^{1}\)\(\Sigma\)\(^{+}\)(b0\(^{+}\)) ↔ X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{1}\)0\(^{+}\),X\(_{2}\)1) transition of NI
Journal of Molecular Spectroscopy, 192 (1) :139-147
1998
Herausgeber: Academic Press

779.

Shestakov, Oleg; Gielen, R.; Setzer, Klaus-Dieter; Fink, Ewald H.
Gas phase LIF study of the b\(^{1}\)\(\Sigma\)\(^{+}\)(b0\(^{+}\)) ↔ X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{1}\)0\(^{+}\),X\(_{2}\)1) transition of NI
Journal of Molecular Spectroscopy, 192 (1) :139-147
1998
Herausgeber: Academic Press

778.

Shestakov, Oleg; Gielen, R.; Setzer, Klaus-Dieter; Fink, Ewald H.
Gas phase LIF study of the b1Σ+(b0+) ↔ X3Σ-(X10+,X21) transition of NI
Journal of Molecular Spectroscopy, 192 (1) :139-147
1998
Herausgeber: Academic Press

777.

Adjiman, C.S.; Schweiger, C.A.; Floudas, C.A.
Handbook of Combinatorial Optimization
In Du, D.-Z. and Pardalos, P. M., Editor
Kapitel Mixed-Integer Nonlinear Optimization in Process Synthesis
Herausgeber: Kluwer Academic Publishers
1998

776.

Kleffmann, J{ö}rg; Becker, Karl Heinz; Wiesen, Peter
Heterogeneous NO\(_{2}\) conversion processes on acid surfaces
Atmospheric Environment, 32 (16) :2721-2729
1998

775.

Kleffmann, J{ö}rg; Becker, Karl Heinz; Wiesen, Peter
Heterogeneous NO\(_{2}\) conversion processes on acid surfaces
Atmospheric Environment, 32 (16) :2721-2729
1998

774.

Kleffmann, Jörg; Becker, Karl Heinz; Wiesen, Peter
Heterogeneous NO2 conversion processes on acid surfaces
Atmospheric Environment, 32 (16) :2721-2729
1998

773.

Ziebarth, K.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
High-resolution study of the X\(_{2}\) \(^{2}\)\(\Pi\)\(_{3/2}\) → X\(_{1}\) \(^{2}\)\(\Pi\)\(_{1/2}\) fine structure transitions of PbF and PbCl
Journal of Molecular Spectroscopy, 191 (1) :108-116
1998
Herausgeber: Academic Press

772.

Ziebarth, K.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
High-resolution study of the X\(_{2}\) \(^{2}\)\(\Pi\)\(_{3/2}\) → X\(_{1}\) \(^{2}\)\(\Pi\)\(_{1/2}\) fine structure transitions of PbF and PbCl
Journal of Molecular Spectroscopy, 191 (1) :108-116
1998
Herausgeber: Academic Press

771.

Ziebarth, K.; Setzer, Klaus-Dieter; Shestakov, Oleg; Fink, Ewald H.
High-resolution study of the X2 2Π3/2 → X1 2Π1/2 fine structure transitions of PbF and PbCl
Journal of Molecular Spectroscopy, 191 (1) :108-116
1998
Herausgeber: Academic Press

770.

Kleffmann, J{ö}rg; Becker, Karl Heinz; Wiesen, Peter
Investigation of the heterogeneous NO\(_{2}\) conversion on perchloric acid surfaces
Journal of the Chemical Society - Faraday Transactions, 94 (21) :3289-3292
1998
Herausgeber: Royal Society of Chemistry

769.

Kleffmann, J{ö}rg; Becker, Karl Heinz; Wiesen, Peter
Investigation of the heterogeneous NO\(_{2}\) conversion on perchloric acid surfaces
Journal of the Chemical Society - Faraday Transactions, 94 (21) :3289-3292
1998
Herausgeber: Royal Society of Chemistry

768.

Kleffmann, Jörg; Becker, Karl Heinz; Wiesen, Peter
Investigation of the heterogeneous NO2 conversion on perchloric acid surfaces
Journal of the Chemical Society - Faraday Transactions, 94 (21) :3289-3292
1998
Herausgeber: Royal Society of Chemistry

767.

Shestakov, Oleg; Gielen, R.; Fink, Ewald H.
LIF Studies of the A\verb=~= \(^{1}\)A' States of BiOH and BiOD
Journal of Molecular Spectroscopy, 192 (1) :111-118
1998
Herausgeber: Academic Press

766.

Shestakov, Oleg; Gielen, R.; Fink, Ewald H.
LIF Studies of the A\verb=~= \(^{1}\)A' States of BiOH and BiOD
Journal of Molecular Spectroscopy, 192 (1) :111-118
1998
Herausgeber: Academic Press

765.

Shestakov, Oleg; Gielen, R.; Fink, Ewald H.
LIF Studies of the A~ 1A' States of BiOH and BiOD
Journal of Molecular Spectroscopy, 192 (1) :111-118
1998
Herausgeber: Academic Press

764.

Shestakov, Oleg; Gielen, R.; Pravilov, A. M.; Setzer, Klaus-Dieter; Fink, Ewald H.
LIF study of the b\(^{1}\)\(\Sigma\)\(^{+}\)(b0\(^{+}\)) ↔ X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{1}\)0\(^{+}\),X\(_{2}\)1) transitions of SbH and SbD
Journal of Molecular Spectroscopy, 191 (1) :199-205
1998
Herausgeber: Academic Press

763.

Shestakov, Oleg; Gielen, R.; Pravilov, A. M.; Setzer, Klaus-Dieter; Fink, Ewald H.
LIF study of the b\(^{1}\)\(\Sigma\)\(^{+}\)(b0\(^{+}\)) ↔ X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{1}\)0\(^{+}\),X\(_{2}\)1) transitions of SbH and SbD
Journal of Molecular Spectroscopy, 191 (1) :199-205
1998
Herausgeber: Academic Press