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

1995: 612.
Mengel, Markus; Jensen, Per
A Theoretical Study of the Stark Effect in Triatomic Molecules: Application to H\(_{2}\)O
Journal of Molecular Spectroscopy, 169 (1) :73-91
1995
Herausgeber: Academic Press
DOI: 10.1006/jmsp.1995.1007; 611.
Mengel, Markus; Jensen, Per
A Theoretical Study of the Stark Effect in Triatomic Molecules: Application to H\(_{2}\)O
Journal of Molecular Spectroscopy, 169 (1) :73-91
1995
Herausgeber: Academic Press
DOI: 10.1006/jmsp.1995.1007; 610.
Mengel, Markus; Jensen, Per
A Theoretical Study of the Stark Effect in Triatomic Molecules: Application to H2O
Journal of Molecular Spectroscopy, 169 (1) :73-91
1995
Herausgeber: Academic Press
DOI: 10.1006/jmsp.1995.1007; 609.
Jensen, Per; Brumm, Martin; Kraemer, Wolfgang P.; Bunker, Philip R.
A Treatment of the Renner Effect Using the MORBID Hamiltonian
Journal of Molecular Spectroscopy, 171 (1) :31-57
1995
Herausgeber: Academic Press
DOI: 10.1006/JMSP.1995.1101; 608.
Jensen, Per; Brumm, Martin; Kraemer, Wolfgang P.; Bunker, Philip R.
A Treatment of the Renner Effect Using the MORBID Hamiltonian
Journal of Molecular Spectroscopy, 171 (1) :31-57
1995
Herausgeber: Academic Press
DOI: 10.1006/JMSP.1995.1101; 607.
Jensen, Per; Brumm, Martin; Kraemer, Wolfgang P.; Bunker, Philip R.
A Treatment of the Renner Effect Using the MORBID Hamiltonian
Journal of Molecular Spectroscopy, 171 (1) :31-57
1995
Herausgeber: Academic Press
DOI: 10.1006/JMSP.1995.1101; 606.
Jensen, Per; Brumm, Martin; Kraemer, Wolfgang P.; Bunker, Philip R.
An ab Initio Calculation of the Rovibronic Energies of the CH\(_{2}\)\(^{+}\) Molecule
Journal of Molecular Spectroscopy, 172 (1) :194-204
1995
Herausgeber: Academic Press
DOI: 10.1006/JMSP.1995.1166; 605.
Jensen, Per; Brumm, Martin; Kraemer, Wolfgang P.; Bunker, Philip R.
An ab Initio Calculation of the Rovibronic Energies of the CH\(_{2}\)\(^{+}\) Molecule
Journal of Molecular Spectroscopy, 172 (1) :194-204
1995
Herausgeber: Academic Press
DOI: 10.1006/JMSP.1995.1166; 604.
Jensen, Per; Brumm, Martin; Kraemer, Wolfgang P.; Bunker, Philip R.
An ab Initio Calculation of the Rovibronic Energies of the CH2+ Molecule
Journal of Molecular Spectroscopy, 172 (1) :194-204
1995
Herausgeber: Academic Press
DOI: 10.1006/JMSP.1995.1166; 603.
Gerstberger, R.; Günther, M.
Charge-oriented extrapolation methods in digital circuit simulation
Applied Numerical Mathematics, 18 (1) :115–125
1995
Herausgeber: Elsevier
DOI: 10.1016/0168-9274(95)00049-Z; 602.
Gerstberger, Robert; Günther, Michael
Charge-oriented extrapolation methods in digital circuit simulation
Applied numerical mathematics, 18 (1-3) :115--125
1995
Herausgeber: North-Holland; 601.
Flaud, Jean-Marie; Camy-Peyret, C.; B{ü}rger, H.; Jensen, Per; Kozin, Igor N.
Experimental evidence for the formation of fourfold rovibrational energy clusters in the \(\nu\)\(_{1}\)/\(\nu\)\(_{3}\) vibrational states of H\(_{2}\)\(^{80}\)Se
Journal of Molecular Spectroscopy, 172 (1) :126-134
1995
Herausgeber: Academic Press
DOI: 10.1006/jmsp.1995.1161; 600.
Flaud, Jean-Marie; Camy-Peyret, C.; B{ü}rger, H.; Jensen, Per; Kozin, Igor N.
Experimental evidence for the formation of fourfold rovibrational energy clusters in the \(\nu\)\(_{1}\)/\(\nu\)\(_{3}\) vibrational states of H\(_{2}\)\(^{80}\)Se
Journal of Molecular Spectroscopy, 172 (1) :126-134
1995
Herausgeber: Academic Press
DOI: 10.1006/jmsp.1995.1161; 599.
Flaud, Jean-Marie; Camy-Peyret, C.; Bürger, H.; Jensen, Per; Kozin, Igor N.
Experimental evidence for the formation of fourfold rovibrational energy clusters in the ν1/ν3 vibrational states of H280Se
Journal of Molecular Spectroscopy, 172 (1) :126-134
1995
Herausgeber: Academic Press
DOI: 10.1006/jmsp.1995.1161; 598.
Heilmann, Margareta
Explicit Voronovskaja-type results for linear combinations of BDT-operators
Approximation Theory and its Applications, 11 (1) :54-61
1995
DOI: 10.1007/BF02836445; 597.
Ehrhardt, M.
Finite Differenzenverfahren für hyperbolische Systeme mit absorbierenden Randbedingungen
Technische Universität Berlin
1995; 596.
Jensen, Per; Li, Yan; Hirsch, Gerhard; Buenker, Robert J.; Lee, Timothy J.; Kozin, Igor N.
Fourfold clusters of rovibrational energies in H\(_{2}\)Te studied with an ab initio potential energy function
Chemical Physics, 190 (2-3) :179-189
1995
DOI: 10.1016/0301-0104(94)00262-9; 595.
Jensen, Per; Li, Yan; Hirsch, Gerhard; Buenker, Robert J.; Lee, Timothy J.; Kozin, Igor N.
Fourfold clusters of rovibrational energies in H\(_{2}\)Te studied with an ab initio potential energy function
Chemical Physics, 190 (2-3) :179-189
1995
DOI: 10.1016/0301-0104(94)00262-9; 594.
Jensen, Per; Li, Yan; Hirsch, Gerhard; Buenker, Robert J.; Lee, Timothy J.; Kozin, Igor N.
Fourfold clusters of rovibrational energies in H2Te studied with an ab initio potential energy function
Chemical Physics, 190 (2-3) :179-189
1995
DOI: 10.1016/0301-0104(94)00262-9; 593.
Breidohr, R.; Shestakov, Oleg; Setzer, Klaus-Dieter; Fink, Ewald H.
High-Resolution Study of the a \(^{3}\)\(\Sigma\)\(^{+}\) (a\(_{1}\) 1) → X \(^{1}\)\(\Sigma\)\(^{+}\) (X 0\(^{+}\)) Transitions of BiP and BiAs
Journal of Molecular Spectroscopy, 172 (2) :369-377
1995
Herausgeber: Academic Press
DOI: 10.1006/JMSP.1995.1185; 592.
Breidohr, R.; Shestakov, Oleg; Setzer, Klaus-Dieter; Fink, Ewald H.
High-Resolution Study of the a \(^{3}\)\(\Sigma\)\(^{+}\) (a\(_{1}\) 1) → X \(^{1}\)\(\Sigma\)\(^{+}\) (X 0\(^{+}\)) Transitions of BiP and BiAs
Journal of Molecular Spectroscopy, 172 (2) :369-377
1995
Herausgeber: Academic Press
DOI: 10.1006/JMSP.1995.1185; 591.
Breidohr, R.; Shestakov, Oleg; Setzer, Klaus-Dieter; Fink, Ewald H.
High-Resolution Study of the a 3Σ+ (a1 1) → X 1Σ+ (X 0+) Transitions of BiP and BiAs
Journal of Molecular Spectroscopy, 172 (2) :369-377
1995
Herausgeber: Academic Press
DOI: 10.1006/JMSP.1995.1185; 590.
Ziebarth, K.; Setzer, Klaus-Dieter; Fink, Ewald H.
High-Resolution Study of the X\(_{2}\) \(^{2}\)\(\Pi\)\(_{1/2}\) → X\(_{1}\) \(^{2}\)\(\Pi\)\(_{3/2}\) Fine-Structure Transitions of \(^{130}\)TeF and \(^{130}\)Te\(^{35}\)Cl
Journal of Molecular Spectroscopy, 173 (2) :488-498
1995
Herausgeber: Academic Press
DOI: 10.1006/jmsp.1995.1251; 589.
Ziebarth, K.; Setzer, Klaus-Dieter; Fink, Ewald H.
High-Resolution Study of the X\(_{2}\) \(^{2}\)\(\Pi\)\(_{1/2}\) → X\(_{1}\) \(^{2}\)\(\Pi\)\(_{3/2}\) Fine-Structure Transitions of \(^{130}\)TeF and \(^{130}\)Te\(^{35}\)Cl
Journal of Molecular Spectroscopy, 173 (2) :488-498
1995
Herausgeber: Academic Press
DOI: 10.1006/jmsp.1995.1251; 588.
Ziebarth, K.; Setzer, Klaus-Dieter; Fink, Ewald H.
High-Resolution Study of the X2 2Π1/2 → X1 2Π3/2 Fine-Structure Transitions of 130TeF and 130Te35Cl
Journal of Molecular Spectroscopy, 173 (2) :488-498
1995
Herausgeber: Academic Press
DOI: 10.1006/jmsp.1995.1251

Index Analysis

Group members working on that field

Cooperations

Publications

612.

611.

610.

609.

608.

607.

606.

605.

604.

603.

602.

601.

600.

599.

598.

597.

596.

595.

594.

593.

592.

591.

590.

589.

588.