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

1979

17.

Barnes, Ian; Becker, Karl Heinz; Fink, Ewald H.
Chemiluminescence of SO(1Δg,1Σg+) sensitized by O2(1Δg)
Chemical Physics Letters, 67 (2-3) :310-313
1979

DOI: 10.1016/0009-2614(79)85168-4

16.

Barnes, Ian; Becker, Karl Heinz; Fink, Ewald H.
Near-infrared emissions from the \(^{1}\)\(\Delta\)\(_{g}\) and \(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) states of S\(_{2}\)
Chemical Physics Letters, 67 (2-3) :314-317
1979

DOI: 10.1016/0009-2614(79)85169-6

15.

Barnes, Ian; Becker, Karl Heinz; Fink, Ewald H.
Near-infrared emissions from the \(^{1}\)\(\Delta\)\(_{g}\) and \(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) states of S\(_{2}\)
Chemical Physics Letters, 67 (2-3) :314-317
1979

DOI: 10.1016/0009-2614(79)85169-6

14.

Barnes, Ian; Becker, Karl Heinz; Fink, Ewald H.
Near-infrared emissions from the 1Δg and 1Σg+ states of S2
Chemical Physics Letters, 67 (2-3) :314-317
1979

DOI: 10.1016/0009-2614(79)85169-6

13.

Tausch, Michael W.
Vorschlag für den Aufbau und die Bewertung einer Klausur zum Kurs ''Bindung und Struktur''
Praxis der Naturwissenschaften (Chemie), 28 :304
1979
1978

12.

Tausch, Michael W.; C. Hass, E.; J. Plath, P.
Eine graphentheoretische Bezugsstruktur für die Eigenwertsumme konjugierter Kohlenwasserstoffe
Bremer Briefe zur Chemie, 2 (30)
1978

11.

Leiss, A.; Schurath, Ulrich; Becker, Karl Heinz; Fink, Ewald H.
Revised quenching rate constants for metastable oxygen molecules O\(_{2}\)(a\(^{1}\)\(\Delta\)\(_{g}\))
Journal of Photochemistry, 8 (2) :211-214
1978

DOI: 10.1016/0047-2670(78)80021-5

10.

Leiss, A.; Schurath, Ulrich; Becker, Karl Heinz; Fink, Ewald H.
Revised quenching rate constants for metastable oxygen molecules O\(_{2}\)(a\(^{1}\)\(\Delta\)\(_{g}\))
Journal of Photochemistry, 8 (2) :211-214
1978

DOI: 10.1016/0047-2670(78)80021-5

9.

Leiss, A.; Schurath, Ulrich; Becker, Karl Heinz; Fink, Ewald H.
Revised quenching rate constants for metastable oxygen molecules O2(a1Δg)
Journal of Photochemistry, 8 (2) :211-214
1978

DOI: 10.1016/0047-2670(78)80021-5

1977

8.

[german] Tausch, Michael W.; Elian, Mihai; Bucur, Aurora; Cior{{\^a}}nescu, Ecaterina
Über das photochemische Verhalten von zwei Tribenzo-(CH)12-Valenzisomeren
Chemische Berichte, 110 (5) :1744-1747
1977
Herausgeber: Wiley

DOI: 10.1002/cber.19771100518

1974

7.

Mihail, R.; Tausch, Michael W.
Homogene Reaktionen in einem Rohrreaktor mit nicht-Newtonscher Strömung
The Chemical Engineering Journal, 7 (1) :53--60
1974
Herausgeber: Elsevier {BV}

DOI: 10.1016/0300-9467(74)80025-0

6.

Becker, Karl Heinz; Fink, Ewald H.; Langen, P.; Schurath, Ulrich
Near infrared emission bands of the HO\(_{2}\) radical
The Journal of Chemical Physics, 60 (11) :4623-4625
1974

DOI: 10.1063/1.1680950

5.

Becker, Karl Heinz; Fink, Ewald H.; Langen, P.; Schurath, Ulrich
Near infrared emission bands of the HO\(_{2}\) radical
The Journal of Chemical Physics, 60 (11) :4623-4625
1974

DOI: 10.1063/1.1680950

4.

Becker, Karl Heinz; Fink, Ewald H.; Langen, P.; Schurath, Ulrich
Near infrared emission bands of the HO2 radical
The Journal of Chemical Physics, 60 (11) :4623-4625
1974

DOI: 10.1063/1.1680950

1973

3.

Becker, Karl Heinz; Fink, Ewald H.; Langen, P.; Schurath, Ulrich
The Chemiluminescent Reaction of HCO with O\(_{2}\)(\(^{1}\)\(\Delta\)\(_{g}\))
Zeitschrift für Naturforschung A, 28 (11) :1872-1874
1973

DOI: 10.1515/zna-1973-1121

2.

Becker, Karl Heinz; Fink, Ewald H.; Langen, P.; Schurath, Ulrich
The Chemiluminescent Reaction of HCO with O\(_{2}\)(\(^{1}\)\(\Delta\)\(_{g}\))
Zeitschrift für Naturforschung A, 28 (11) :1872-1874
1973

DOI: 10.1515/zna-1973-1121

1.

Becker, Karl Heinz; Fink, Ewald H.; Langen, P.; Schurath, Ulrich
The Chemiluminescent Reaction of HCO with O2(1Δg)
Zeitschrift für Naturforschung A, 28 (11) :1872-1874
1973

DOI: 10.1515/zna-1973-1121