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
- 1982
50.
Jensen, Per; Brodersen, Svend
The \(\nu\)\(_{5}\) Raman band of CH\(_{3}\)CD\(_{3}\)
Journal of Raman Spectroscopy, 12 (3) :295-299
198249.
Jensen, Per; Bunker, Philip R.; Hoy, A. R.
The equilibrium geometry, potential function, and rotation?vibration energies of CH\(_{2}\) in the X\verb=~=\(^{3}\)B\(_{1}\) ground state
The Journal of Chemical Physics, 77 (11) :5370-5374
198248.
Jensen, Per; Bunker, Philip R.; Hoy, A. R.
The equilibrium geometry, potential function, and rotation?vibration energies of CH\(_{2}\) in the X\verb=~=\(^{3}\)B\(_{1}\) ground state
The Journal of Chemical Physics, 77 (11) :5370-5374
198247.
Jensen, Per; Bunker, Philip R.; Hoy, A. R.
The equilibrium geometry, potential function, and rotation?vibration energies of CH2 in the X~3B1 ground state
The Journal of Chemical Physics, 77 (11) :5370-5374
198246.
Jensen, Per; Bunker, Philip R.
The geometry and the inversion potential function of formaldehyde in the and electronic states
Journal of Molecular Spectroscopy, 94 (1) :114-125
198245.
Jensen, Per; Bunker, Philip R.
The geometry and the inversion potential function of formaldehyde in the and electronic states
Journal of Molecular Spectroscopy, 94 (1) :114-125
198244.
Jensen, Per; Bunker, Philip R.
The geometry and the inversion potential function of formaldehyde in the and electronic states
Journal of Molecular Spectroscopy, 94 (1) :114-125
198243.
Jensen, Per; Bunker, Philip R.
The geometry and the out-of-plane bending potential function of thioformaldehyde in the A\verb=~=\(^{1}\)A\(_{2}\) and a\verb=~=\(^{3}\)A\(_{2}\) electronic states
Journal of Molecular Spectroscopy, 95 (1) :92-100
198242.
Jensen, Per; Bunker, Philip R.
The geometry and the out-of-plane bending potential function of thioformaldehyde in the A\verb=~=\(^{1}\)A\(_{2}\) and a\verb=~=\(^{3}\)A\(_{2}\) electronic states
Journal of Molecular Spectroscopy, 95 (1) :92-100
198241.
Jensen, Per; Bunker, Philip R.
The geometry and the out-of-plane bending potential function of thioformaldehyde in the A~1A2 and a~3A2 electronic states
Journal of Molecular Spectroscopy, 95 (1) :92-100
198240.
Jensen, Per; Brodersen, Svend
The ν5 Raman band of CH3CD3
Journal of Raman Spectroscopy, 12 (3) :295-299
198239.
Tausch, Michael W.; J. Plath, P.
Umlagerungen in (CH)₇⁺-Carbokationen
Revue Roumaine de Chimie, 27 :953
1982- 1981
38.
Tausch, Michael W.
BINDUNG UND STRUKTUR - Unterrichtsbuch für die gymnasiale Oberstufe
Herausgeber: Schöningh, Paderborn
198137.
Jensen, Per; Brodersen, Svend; Guelachvili, Guy
Determination of A\(_{0}\) for CH\(_{3}\)\(^{35}\)Cl and CH\(_{3}\)\(^{37}\)Cl from the \(\nu\)\(_{4}\) infrared and Raman bands
Journal of Molecular Spectroscopy, 88 (2) :378-393
198136.
Jensen, Per; Brodersen, Svend; Guelachvili, Guy
Determination of A\(_{0}\) for CH\(_{3}\)\(^{35}\)Cl and CH\(_{3}\)\(^{37}\)Cl from the \(\nu\)\(_{4}\) infrared and Raman bands
Journal of Molecular Spectroscopy, 88 (2) :378-393
198135.
Jensen, Per; Brodersen, Svend; Guelachvili, Guy
Determination of A0 for CH335Cl and CH337Cl from the ν4 infrared and Raman bands
Journal of Molecular Spectroscopy, 88 (2) :378-393
198134.
Barnes, Ian; Bastian, V.; Becker, Karl Heinz; Fink, Ewald H.; Zabel, Friedhelm
Rate constant of the reaction of OH with HO\(_{2}\)NO\(_{2}\)
Chemical Physics Letters, 83 (3) :459-464
198133.
Barnes, Ian; Bastian, V.; Becker, Karl Heinz; Fink, Ewald H.; Zabel, Friedhelm
Rate constant of the reaction of OH with HO\(_{2}\)NO\(_{2}\)
Chemical Physics Letters, 83 (3) :459-464
198132.
Barnes, Ian; Bastian, V.; Becker, Karl Heinz; Fink, Ewald H.; Zabel, Friedhelm
Rate constant of the reaction of OH with HO2NO2
Chemical Physics Letters, 83 (3) :459-464
198131.
Tausch, Michael W.
THEORETISCHE UND EXPERIMENTELLE UNTERSUCHUNGEN VON VALENZISOMERISIERUNGEN
Herausgeber: Minerva Publikation, München
198130.
Tausch, Michael W.
Vorschlag für den Aufbau und die Bewertung einer Klausur zum Kurs ''Grundreaktionen in der organischen Chemie"
Praxis der Naturwissenschaften (Chemie), 30 :374
1981- 1980
29.
Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) → X\(^{3}\)\(\Sigma\)\(^{-}\) Emissions of SeO, SeS, and Se\(_{2}\) in the near infrared
Chemical Physics Letters, 73 (2) :297-303
198028.
Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) → X\(^{3}\)\(\Sigma\)\(^{-}\) Emissions of SeO, SeS, and Se\(_{2}\) in the near infrared
Chemical Physics Letters, 73 (2) :297-303
198027.
Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ → X3Σ- Emissions of SeO, SeS, and Se2 in the near infrared
Chemical Physics Letters, 73 (2) :297-303
198026.
Kauppinen, Jyrki; Jensen, Per; Brodersen, Svend
Determination of the B\(_{0}\) constant of C\(_{6}\)H\(_{6}\)
Journal of Molecular Spectroscopy, 83 (1) :161-174
1980
