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

1981: 30.
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
1981
DOI: 10.1016/0009-2614(81)85501-7
1980: 29.
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
DOI: 10.1016/0022-2852(80)90318-5; 28.
Kauppinen, Jyrki; Jensen, Per; Brodersen, Svend
Determination of the B0 constant of C6H6
Journal of Molecular Spectroscopy, 83 (1) :161-174
1980
DOI: 10.1016/0022-2852(80)90318-5; 27.
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
1980
DOI: 10.1016/0009-2614(80)80376-9; 26.
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
DOI: 10.1016/0022-2852(80)90318-5; 25.
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
1980
DOI: 10.1016/0009-2614(80)80376-9; 24.
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
1980
DOI: 10.1016/0009-2614(80)80376-9
1979: 23.
Glaschick-Schimpf, I.; Leiss, A.; Monkhouse, Penelope B.; Schurath, Ulrich; Becker, Karl Heinz; Fink, Ewald H.
A kinetic study of the reactions of HO\(_{2}\)/DO\(_{2}\) radicals with nitric oxide using near-infrared chemiluminescence detection
Chemical Physics Letters, 67 (2-3) :318-323
1979
DOI: 10.1016/0009-2614(79)85170-2; 22.
Glaschick-Schimpf, I.; Leiss, A.; Monkhouse, Penelope B.; Schurath, Ulrich; Becker, Karl Heinz; Fink, Ewald H.
A kinetic study of the reactions of HO\(_{2}\)/DO\(_{2}\) radicals with nitric oxide using near-infrared chemiluminescence detection
Chemical Physics Letters, 67 (2-3) :318-323
1979
DOI: 10.1016/0009-2614(79)85170-2; 21.
Glaschick-Schimpf, I.; Leiss, A.; Monkhouse, Penelope B.; Schurath, Ulrich; Becker, Karl Heinz; Fink, Ewald H.
A kinetic study of the reactions of HO2/DO2 radicals with nitric oxide using near-infrared chemiluminescence detection
Chemical Physics Letters, 67 (2-3) :318-323
1979
DOI: 10.1016/0009-2614(79)85170-2; 20.
Tausch, Michael W.; C. Ha{ßs}, E.; J. Plath, P.
Beschreibung von Valenzisomerisierungen durch Strukturvariation auf vollständigen Graphen
Informal Communications in Mathematical Chemistry (MatCh), 7 :289
1979; 19.
Barnes, Ian; Becker, Karl Heinz; Fink, Ewald H.
Chemiluminescence of SO(\(^{1}\)\(\Delta\)\(_{g}\),\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\)) sensitized by O\(_{2}\)(\(^{1}\)\(\Delta\)\(_{g}\))
Chemical Physics Letters, 67 (2-3) :310-313
1979
DOI: 10.1016/0009-2614(79)85168-4; 18.
Barnes, Ian; Becker, Karl Heinz; Fink, Ewald H.
Chemiluminescence of SO(\(^{1}\)\(\Delta\)\(_{g}\),\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\)) sensitized by O\(_{2}\)(\(^{1}\)\(\Delta\)\(_{g}\))
Chemical Physics Letters, 67 (2-3) :310-313
1979
DOI: 10.1016/0009-2614(79)85168-4; 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 1Δg and 1Σg+ states of S2
Chemical Physics Letters, 67 (2-3) :314-317
1979
DOI: 10.1016/0009-2614(79)85169-6; 14.
Tausch, Michael W.
Vorschlag für den Aufbau und die Bewertung einer Klausur zum Kurs ''Bindung und Struktur''
Praxis der Naturwissenschaften (Chemie), 28 :304
1979; 13.
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
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

Index Analysis

Group members working on that field

Cooperations

Publications

30.

29.

28.

27.

26.

25.

24.

23.

22.

21.

20.

19.

18.

17.

16.

15.

14.

13.

12.

11.

10.

9.

8.

7.

6.