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

1982

57.

Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ and a1Δ emissions from group VI-VI diatomic molecules: b0+ → X10+, X21 emissions of TeO and TeS
Journal of Molecular Structure, 80 :75-82
1982

DOI: 10.1016/0022-2860(82)87210-4

56.

Kruse, H.; Winter, R.; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ emissions from group V-VII diatomic molecules: b0+ → X10+, X20+ emissions of SbBr
Chemical Physics Letters, 93 (5) :475-479
1982

DOI: 10.1016/0009-2614(82)83223-5

55.

Tausch, Michael W.
Modelle im Chemieunterricht
Der mathematische und naturwissenschaftliche Unterricht (MNU), 35 :226
1982

54.

Becker, Karl Heinz; Horie, O.; Schmidt, V. H.; Wiesen, Peter
Spectroscopic identification of C\(_{2}\)O radicals in the C\(_{3}\)O\(_{2}\) + O flame system by laser-induced fluorescence
Chemical Physics Letters, 90 (1) :64-68
1982

DOI: 10.1016/0009-2614(82)83326-5

53.

Becker, Karl Heinz; Horie, O.; Schmidt, V. H.; Wiesen, Peter
Spectroscopic identification of C\(_{2}\)O radicals in the C\(_{3}\)O\(_{2}\) + O flame system by laser-induced fluorescence
Chemical Physics Letters, 90 (1) :64-68
1982

DOI: 10.1016/0009-2614(82)83326-5

52.

Becker, Karl Heinz; Horie, O.; Schmidt, V. H.; Wiesen, Peter
Spectroscopic identification of C2O radicals in the C3O2 + O flame system by laser-induced fluorescence
Chemical Physics Letters, 90 (1) :64-68
1982

DOI: 10.1016/0009-2614(82)83326-5

51.

Jensen, Per; Brodersen, Svend
The \(\nu\)\(_{5}\) Raman band of CH\(_{3}\)CD\(_{3}\)
Journal of Raman Spectroscopy, 12 (3) :295-299
1982

DOI: 10.1002/jrs.1250120318

50.

Jensen, Per; Brodersen, Svend
The \(\nu\)\(_{5}\) Raman band of CH\(_{3}\)CD\(_{3}\)
Journal of Raman Spectroscopy, 12 (3) :295-299
1982

DOI: 10.1002/jrs.1250120318

49.

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
1982

DOI: 10.1063/1.443785

48.

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
1982

DOI: 10.1063/1.443785

47.

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
1982

DOI: 10.1063/1.443785

46.

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
1982

DOI: 10.1016/0022-2852(82)90298-3

45.

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
1982

DOI: 10.1016/0022-2852(82)90298-3

44.

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
1982

DOI: 10.1016/0022-2852(82)90298-3

43.

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
1982

DOI: 10.1016/0022-2852(82)90241-7

42.

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
1982

DOI: 10.1016/0022-2852(82)90241-7

41.

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
1982

DOI: 10.1016/0022-2852(82)90241-7

40.

Jensen, Per; Brodersen, Svend
The ν5 Raman band of CH3CD3
Journal of Raman Spectroscopy, 12 (3) :295-299
1982

DOI: 10.1002/jrs.1250120318

39.

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
1981

37.

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
1981

DOI: 10.1016/0022-2852(81)90188-0

36.

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
1981

DOI: 10.1016/0022-2852(81)90188-0

35.

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
1981

DOI: 10.1016/0022-2852(81)90188-0

34.

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
1981

DOI: 10.1016/0009-2614(81)85501-7

33.

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
1981

DOI: 10.1016/0009-2614(81)85501-7