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
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 Press777.
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
1998776.
Kleffmann, Jörg; Becker, Karl Heinz; Wiesen, Peter
Heterogeneous NO\(_{2}\) conversion processes on acid surfaces
Atmospheric Environment, 32 (16) :2721-2729
1998775.
Kleffmann, Jörg; Becker, Karl Heinz; Wiesen, Peter
Heterogeneous NO\(_{2}\) conversion processes on acid surfaces
Atmospheric Environment, 32 (16) :2721-2729
1998774.
Kleffmann, Jörg; Becker, Karl Heinz; Wiesen, Peter
Heterogeneous NO2 conversion processes on acid surfaces
Atmospheric Environment, 32 (16) :2721-2729
1998773.
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 Press772.
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 Press771.
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 Press770.
Kleffmann, Jörg; 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 Chemistry769.
Kleffmann, Jörg; 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 Chemistry768.
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 Chemistry767.
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 Press766.
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 Press765.
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 Press764.
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 Press763.
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 Press762.
Shestakov, Oleg; Gielen, R.; Pravilov, A. M.; Setzer, Klaus-Dieter; Fink, Ewald H.
LIF study of the b1Σ+(b0+) ↔ X3Σ-(X10+,X21) transitions of SbH and SbD
Journal of Molecular Spectroscopy, 191 (1) :199-205
1998
Herausgeber: Academic Press761.
Bartel, A.
MultiROW within P-Star. A Feasibility Study
Unclassified NatLab Report No. 1998/824
Herausgeber: Philips Electronics
1998760.
Gilg, A
Numerical circuit simulation Grund, F, s Borchardt, J Gunther, M, s Gilg, A
Surveys on Mathematics for Industry, 8 (3) :165--170
1998
Herausgeber: Wien; New York: Springer-Verlag, 1991-c2005.759.
Le Tallec, P; Perlat, JP; Struckmeier, J
Numerical modeling of gas flows in the transition between rarefied and continuum regimes
Numerical Flow Simulation I: CNRS-DFG Collaborative Research Programme, Results 1996--1998 :222--241
1998
Herausgeber: Springer Berlin Heidelberg758.
Wöhrle, D.; Tausch, Michael W.; Stohrer, W.-D.
PHOTOCHEMIE - Konzepte, Methoden, Experimente
Herausgeber: Wiley-VCH, Weinheim
1998757.
Schmidt, Sven; Benter, Thorsten; Schindler, Ralph N.
Photodissociation dynamcis of ClO radicals in the range (237<λ<270) nm and at 205 nm and the velocity distribution of O(1D) atoms
Chemical Physics Letters, 282 (3-4) :292-298
1998756.
Schmidt, Sven; Benter, Thorsten; Schindler, Ralph N.
Photodissociation dynamcis of ClO radicals in the range (237
Chemical Physics Letters, 282 (3-4) :292-298
1998755.
Schmidt, Sven; Benter, Thorsten; Schindler, Ralph N.
Photodissociation dynamcis of ClO radicals in the range (237
Chemical Physics Letters, 282 (3-4) :292-298
1998754.
Günther, Michael
Simulating digital circuits numerically - a charge-oriented ROW approach
Numerische Mathematik, 79 (2) :203–212
1998
Herausgeber: Springer New York
